Condense the expression to the logarithm of a single quantity In x - [In(x 1) In(x - 1)1

Q: Find the domain of the logarithmic function :  f(x) = ln(x2 - x - 2)

A: Inside log we can not have negative number. So, x2 - x - 2>0

Q: . In the definition of the logarithmic function, the base a is notallowed to equal 1. Why?

A: In the definition of the logarithmic function, the base a is not   allowed to equal 1. Why?

Q: (b) For what value of x is log₂ (x+1)-log₂ (x-1)=3?

A:

Q: If the graph of a logarithmic function f(x) = loga x, wherea > 0 and a ≠ 1, is increasing, then…

A: Since in logarithmic function value should be positive. Therefore, in fx=logax the value of x must…

Q:

A: By definition, The logarithmic function y=logax is defined to be equivalent to the exponential…

Q: Write the expression as a logarithm of a single quantity.

A: To write: The expression gx=2ln x-ln 4 as a logarithm of single quantity. Given: The expression…

Q: Condense the expression to the logarithm of a single quantity. 4 log (x) log4(y) - 3 log4(z)

A: Given query is to compress the logarithmic expression.

Q: The graph of every logarithmic function f(x) = loga x, wherea >0 and a ≠ 1, passes through three…

A: Points for the logarithmic functions can be found with the help of the arbitrary points. Put such…

Q: What is the solution set for x in the logarithmic equation of log3(x-9) - log3 x=3

A:

Q: Condense the expression to the logarithm of a single quantity. ln x − [ln(x + 1) + ln(x − 1)]

A:

Q: Find the domain of the logarithmic function f(x) = ln(x - 1)2.

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Write the expression as a logarithm of a single quantity. + In(x + 5) – 3 In(1 + Vx) 2

A: Given expression is ln6+12lnx+5-3ln1+x We have to write given expression as a logarithm of a single…

Q: Condense the expression to the logarithm of a single quantity. [3 In(x + 5) + In(x) – In(x3 - 1)] 2

A: The given expression,        123 lnx+5+lnx-lnx3-1

Q: Use the properties of natural logarithms to simplify the function. f(x) = In(e-6x) + 9x + In(1) f(x)…

A:

Q: Condense the expression to the logarithm of a single quantity. 2 In(8) - 4 In(z - 6)

A:

Q: Condense the expression to the logarithm of a single quantity. 3 In(4) 8 In(z - 6)

A: Solution-

Q: Vx*+12 In (x+16)/x-3

A: Given,                   lnx4+123x+16x-3=?

Q: Find the domain of the logarithmic function : f(x) = log5(x + 6)

A:

Q: Condense the expression to the logarithm of a single quantity. [9 In(x + 4) + In(x) – In(xº – 8)]

A:

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: Condense the expression to the logarithm of a single quantity. 3 log3(x) +log3(y) - 8 log3(z) X

A:

Q: Condense the expression to the logarithm of a single quantity. [3 In(x + 5) + In(x) – In(x3 - 8)]

A:

Q: Write the expression as a logarithm of a single quantity.                               2[ln x −…

A:

Q: Evaluate the logarithm at the given value of x without using a calculator. Function Value g(x) =…

A:

Q: Evaluate the logarithm at the given value of x without using a calculator. Function Value g(x) =…

A: Given:- g(x)=logb(x)  Evaluate g(x) at x=√b

Q: Find the domain of the logarithmic function : f(x) = log(7 - x)

A: Domain of any function is defined as the value of x for which the function is defined - Given…

Q: Find the domain of the logarithmic function f(x) = log5(x + 4).

A: Given:log5x+4

Q: Find the domain of the logarithmic function f(x) = log5(x + 6).

A: Given:fx=log5x+6

Q: Find the domain of the logarithmic function f(x) = log8(x + 5).

A: To find domain of the logarithmic function fx=log8x+5

Q: The change-of-base formula states that log, x can be written as a ratio of logarithms with base a as…

A: We have to change the base of the given logarithm  we have,  logbx

Q: Find the domain of the logarithmic function : f(x) = ln(x - 7)2

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Evaluate the logarithm at the given value of x without using a calculator. Function Value g(x) =…

A: .To evaluate the logarithm at the given value of x without using a calculator.Function…

Q: Find the domain of the logarithmic function : f(x) = log5(x + 4)

A: Given expression, fx=log5x+4 The domain of fx=log5x+4 is given by gx>0 Then, the domain of f…

Q: Condense the expression to the logarithm of a single quantity. 5 In(2) – 9 In(z - 3)

A: use logarithm identity:-                (i)  nln(m) = ln(m)n                (ii)  ln(m)-ln(n) = lnmn

Q: Write the expression as a logarithm of a single ex 1 4 In x- In y 4 Iny-D] 4 In x- %3D 4

A: Using power rule and quotient rule of logarithm,

Q: [4 In(x + 8) + In(x) – In(x* - 9)]

A:

Q: Expand the logarithimic expression.

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

Q: Condense the expression to the logarithm of a single quantity. log x −2log(x +1)

A: Given,

Q: Write the expression as a logarithm of a single quantity. [In(x2 – 1) – In(x + 1) + In(x – 1)]

A: The solution of the second problem is given in the next step.

Q: Condense the expression to the logarithm of a single quantity. 6 In(2) – 3 In(z - 9)

A: Logarithmic Rules: logbMk=k logbM logbMN=logbM-logbN   6 log2-3logz-9 = log26-log(z-9)3 6…

Q: Condense the expression to the logarithm of a single quantity. 2 In (5) - 8 In(z - 6)

A:

Q: Condense the logarithmic expression. 2 In 5 + 2 In x – In y=||

A:

Q: Use the laws of logarithms to expand and simplify the expression. x3 In x (1+x)5) () In (1+x)5

A: We have to simplify the given log function.

Q: Condense the expression to the logarithm of a single quantity. [9 In(x + 5) + In(x) – In(x° – 4)] 2

A:

Q: Find the domain of the logarithmic function f(x) = log(2 - x).

A: Consider the given logarithmic function fx=log2-x

Q: Condense the expression to the logarithm of a single quantity. 1 -[8 In(x + 2) + In(x) – In(x8 – 5)]…

A:

Q: Change the logarithmic statement to an equivalent statement involving an exponent. ln 4 = x

A: Since, we have to change the logarithmic statement ln 4=x into an equivalent statement involving an…

Q: Use the definition of the logarithmic function to find x. In x = -1 In (1/e) = x %3D

A: First Part: Given, lnx=-1x=e-1lnex=a⇒x=eax=1e