Expand the following logarithm so that it contains no products, quotients, or powers. e2x+3 a. In [(9x+e)* ] 3/2

Q: 6. Simplify each of the following using the properties of logarithms: (a) In () (b) log2(VE5) 8y3

A:

Q: Express the following logarithms in terms of ln 2 and ln 3.c. ln (1/2)           d. ln( 9)^1/3

A: Given: c  ln12  d ln913 Formula Used: 1 lnmn=lnm-lnn2 lnxn=nlnx

Q: Expand the following expression using the properties of the logarithms. Assume x and y are positive.…

A: Consider x,y>0 . Properties of logarithm:  Product rule : ln xy=ln x+ln y Quotient rule :…

Q: Express the following logarithms in terms of ln 2 and ln 3.a. ln 0.75                 b. ln (4/9)

A: (a) ln 0.75 = ln (3/4) = ln 3 - ln 4 = ln 3 - ln 22 = ln 3 - 2 ln 2 Hence the answer.

Q: 15) Use the properties of logarithms to rewrite each 2 a. In c. In 5y b. In Vr+2 d. In ¤(x +1)´

A: Explanation and solutions is given below....

Q: Write as a single term that does not contain a logarithm:

A: eln 8 x5- ln 2 x2

Q: log, (x³y?) + log3 x 27 log, (x³y²) + log3 x²y

A:

Q: Which of the following is an equivalent exponential expression of log1(x) =..-1 (A) (-1)"=- 3 (B)…

A: The given expression,log13(x)=-1

Q: Use the properties of logarithms to expand the given expression as much as possible

A: Use division property of logarithm

Q: condense the following expression into a single logartithm whose base is 4.  3log4X-log2Y+2

A: It is a logarithmic problem

Q: In + 1

A:

Q: (1) Expand the following into as many logarithms as possible, with what's inside each simple as…

A:

Q: Use the properties of logarithms, given that In(2) = 0.6931 and In(5) 1.6094, to approximate the…

A:

Q: Solve the following equations for xx using the natural logarithm:  11⋅4^x=2e^−3x

A:

Q: Suppose that In 2 = a and In 5 =b. Use properties of logarithms to write each  logarithm in terms of…

A: Given- ln2=a and ln5=b To find- The expression in the terms of a and b. Formula used- lnm·n=lnm-lnn…

Q: Expand the following logarithm into the sum/difference of multiple logarithms in their simplest…

A:

Q: Suppose that In 2=a andIn3=b. Use properties of logarithms to write each logarithm in terms of a and…

A: Given: ln2=aln3=b

Q: Express the given quantity as a single logarithm. - In(x + 2)5 + In x – In(x2 + 3x + 2)²|

A: The exponent 5 becomes the coefficient

Q: Write down the formula of the change of base theorem and briefly state what it is used for.   3b)…

A: The change of base theorem:

Q: Complete the following table by rewriting the given exponential expressions to logarithmic form…

A: In this question, we need to complete the table by converting the given exponential expression to…

Q: Express the following logarithms in terms of ln 2 and ln 3. ln √13.5

A: Express ln13.5 in terms of ln2 and ln3.

Q: Determine the expanded form of the following log expression log5(x^-7y^5/z^10)

A: We need to determine the expanded form of the following log expression log5x-7y5z10. So,…

Q: Express the following as a sum, difference, or multiple of logarithms. log 2 a

A:

Q: Express the following expression as an equivalent expression that is a single logarithm. 2 logbx+7…

A:

Q: Expand the following logarithmic expression as much as possible: (x + 3)*(x² – 4) V5 – x - In

A:

Q: Express the given quantity as a single logarithm In(x 2)7 In x In(x23x 2)2 2

A: Make the coefficients into exponent. And they will multiply with the existing exponents.

Q: Which shows the expression In 4 - 2ln x written as a single logarithm.

A: Given expression is 12ln 4 - 2 ln x write it in single logarithm

Q: Express the following logarithms in terms of ln 2 and ln 3. ln 3√2

A: Solution:- the given term is A=ln(32) as we know that  ln(m×n)=lnm+lnnand ln(a)b=bln(a)

Q: write the given in ter ms of 3 to any base log f64 A.

A:

Q: Fully expand the following logarithmic expression into a sum and/or difference of logarithms of…

A: We know that,ln(m)+ln(n)=ln(mn)ln(m)-ln(n)=ln(mn)ln(mn)=nln(m)Here…

Q: 3 [og,x + logy] – 2[log,a + log, V5]

A:

Q: (8) Expand the following into as many logarithms as possible, with what's inside each logarithm as…

A:

Q: Determine whether the following statement is true or not : Log(-1+431) =2Log(-1+/ãi)

A: Proceed as shown

Q: Express the following sum and/or difference of logarithms as a single logarithm. 2 loga y+logs -…

A:

Q: 7) use the properties of logarithms to: a, expand the expression log(x3z y2)

A: Consider the given expression log(x3z y2)

Q: Express the following logarithms in terms of ln 5 and ln 7. ln 9.8

A: The given expression is ln 9.8

Q: Expand the logarithimic expression.

A: Given: y=lnx2-1x2+1 We know that lnmn=nlnm…

Q: 1. Use the properties of the natural logarithms to simplify the following expressions: c) In(4t*) –…

A: To simplify12ln(4t4)-ln2

Q: Suppose that In 5 = a and In 11 = b. Use properties of logarithms to write the logarithm in terms of…

A:

Q: Express the given quantity as a single logarithm. - In(x + 2)5 + In(x) – In(x² + 3x + 2)=

A: We have to simplyfing this

Q: 1. Use the properties of the natural logarithms to simplify the following expressions: b) In(3x² –…

A: ln3x2-9x+ln13x

Q: Simplify the following into a single logarithm:2log(8) + 2log(x)

A:

Q: Condense the following log expression. -2log3(xy)+4/5log3(z)^10+log3(x+1)

A: Condensing the logarithmic expression.

Q: Which of the following would is a Step in solving for x ? %3D log2 (8x) + log, (3x- 5) = 3 O log,…

A: We have to find the step which is involving in solving for x: log28x+log23x-5=3 We know the product…

Q: 13. Combine the following into a single logarithm Inz- 3 In (z + 4) + In (y)) 112

A: Follow the steps.

Q: Express the given quantity as a single logarithm. In(a + b) + In(a - b) – 3 In(c)

A: Given  ln(a+b) + ln(a-b) - 3 ln c  = ln [ (a+b)(a-b) ] - 3 ln c   = ln ( [ (a+b)(a-b) ] / c ) ln a +…

Q: Expand the following using the properties of logarithms and simplify. Assume when necessary that all…

A: Given logarithm is:As per the properties of logarithms,Using the above properties and then…

Q: Use the Laws of Logarithms to expand the expression. (a) log (xy5 (b) In x + 2 ,3v2 (c) log x3(x2 +…

A: values = ?

Q: Express the following logarithms in terms of ln 2 and ln 3. ln 3√9

A: To express:  ln 3√9 in terms of  ln 2 and ln 3.

Q: * Suppose that In 2 = a In 3 = b. Use properties of logarithms to write the logarithm in terms of a…

A: Properties: