Expand into several logarithms: x² y? In z5

Q: Express as a single logarithm. 5log,m- log,n

A: The rules one have to use in this question are logam-logan=logamnalogbm=logbma

Q: Condense the following into a single logarithm } log, 8 – log, (3ª – 8)

A: Answer is given in next step.

Q: Express the equation in logarithmic form. (a)    32x = 10   (b)    10−2x = 0.1

A:

Q: use logarithmic difterient iation to Aind r V3x-1

A:

Q: Express the equation in logarithmic form. (a)    32x = 10   b)   10−2x = 0.1

A: To express the given equations in logarithmic form.

Q: xvx² – 1 In (х — 3)

A: Given,           lnxx2-1x-32

Q: Express as a single logarithm. 3log6x + 5log,(x - 6)

A:

Q: Expand the logarithmic expression. 2x4 In y7

A: According to the natural logarithm quotient rule, . According to the natural logarithm product rule,…

Q: Pls help

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Q: Express the given quantity as a single logarithm. In(a + b) + In(a - b) – 8 In(c)

A:

Q: 2 In x - In y + 1 5

A: we know that logarithmic properties :  1 ). ln ( a • b ) =ln ( a ) + ln ( b )  2 )  ln ( a n ) = n…

Q: Convert 6x = y to an equivalent statement involving a logarithm.

A: Given, 6x = y Aim to convert into equivalent statement involving a logarithm.

Q: Condense Conden se into a single logarithm. 4) 6log § x – 31og § y 4.

A: Given 6log8x-3log8y

Q: Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as…

A:

Q: express as one logarithm with a coefficient of 1:3log a/x+log b/y -2log c/z

A: Solution is given below:

Q: . Express as a single logarithm: loga x + loga(x² – 16) – loga7 – log.(x- 4).

A: The given expression is logax+logax2-16-loga7-logax-4. We have to express single logarithm. To solve…

Q: Expand the following logarithm as much as possible. ,2.3 x*y log7

A: Solve the following

Q: ewrite as a single log. log,2x+3(loga X- log.y)

A:

Q: Combine into a single logarithm.

A: 32log2x-y-2log2x2+y2

Q: Expand the logarithm and simplify as much as possible. 3y4 log, () =

A: We have to solve given expression.

Q: Write y=x+ in logarithmic form

A: Using the properties of the logarithmic functions, we can write that: log ab=blog alogab=log blog a

Q: Solve for a positive value of x. log,(x) = 2

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Q: Find x using logarithmic rules. 2.6x = 4x+1

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Q: If ex = 5, write x in terms of the natural logarithm.

A: Given ex=5 To write x in terms of the natural logarithm.

Q: Combine into a singel logarithm 3/2In(x-y)-2In(x^2+y^2

A: Recall: lnmn = n lnm lnmn= lnm+lnn lnmn= lnm-lnn

Q: .Condense the logarithmic expres 3 log5 3x + 2log5 (x - 2)

A:

Q: condense to a single logarithm: 2log4c + log4a / 2

A: We have to solve given expression for single logarithm.

Q: ху Write in terms of x and y: log (x. Vxy

A:

Q: Write as a single logarithm: 2 ln x + 1/3 ln(x + 5)

A: The given expression is 2lnx+13lnx+5

Q: Condense the expression into a single logarithm. log, (w) 7 log, (x) – 2 log, (y) 3

A:

Q: Use the One-to-One property to solve for x: log, (x + 2x) = log, (3x + 2).

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Q: Write as sum and difference of simpler logarithms. 1. In *(r-2)s V3x-4

A:

Q: Write the logarithm in expanded form. log3((x®y)®)

A:

Q: Write as a single logarithm. 1- log(x)

A: Given,          1-logx

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

A: Condensing the logarithmic expression.

Q: )Solve for y in terms of r. log, y = log, r – log, 10 + log, 6

A: Given, logby = logbx - logb10 + logb6 Solving the above equation using the properties of logarithm

Q: Solve by using logarithm X+3 2-X 2. 13D

A:

Q: Write as a single logarithm and simplify. In(x+1) + In(x-1)-2lnx

A: Hh

Q: Express as a single logarithm. log c(40) - log (5)

A:

Q: Solve for x. -8+ log, (x+4)=-6

A: Given -8+log5(x+4)=-6 Or, log5(x+4)=8-6=2 Or, (x+4)=52  [since loga(x)=m, then x=am] Or, x+4=25 Or,…

Q: Write as a single logarithm and simplify if possible. 1. In(x²) – 4 In(y) – 61n(x³/2)+ 3ln(2y²)

A: This question can be solved using the properties of logarithm.

Q: Simplify. Enter the result as a single logarithm with a coefficient of 1. log, (92) + log, (6z?)

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Q: Use the fact that: loga (x) = -3.4, loga (y) = 4.3, and loga (z) = 6.2 to evaluate the following:…

A:

Q: Use logarithms to solve. e2x – ex – 90 = 0 %3D -

A: Solve: e2x - ex -90=0

Q: Find the logarithm. lor, (2:)-[ log2

A:

Q: Write as one logarithm: 13ln(x−1)−12ln(x+1)+2lnx.

A: The given expression is 13ln(x−1)−12ln(x+1)+2lnx   Apply log rule:…

Q: Solve for x : log, x = 4

A: Here we use basic logarithmic properties to solve the given equation

Q: Expand each logarithm. log, (r . y - 2')

A: Given,           log3x·y·z3

Q: Expand the logarithimic expression.

A: log4x3y2x-15

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.