Question

Which equation has x=-6 as the solution? A-logx36=2. B-log3(2x-9)=3. C-log3 216=x. D-log3(-2x-3)=2

Answer 1

I posted this to your other question as well:

So we have:

A) $\log_x(36)=2$

B) $\log_3(2x-9)=3$

C) $\log_3(216)=x$

D) $\log_3(-2x-3)=2$

We need to try x = –6 in each equation until we find a solution that makes both sides of the equation equal.

For A, this gives an undefined result. Logarithms are only defined for bases that are positive real numbers not equal to 1.

For B, this again gives an undefined result. The logarithm of a number is only defined when that number is a positive real number. It would be –21, which is undefined.

For C, we have a defined operation, but $\log_3(216)=4.893 \neq -6$.

Finally, for D, we have 

$\log_3(-2(-6)-3)=2\\ \log_3(9)=2 \\ 3^2=9 \\ 9=9$

This is true.

Answer 2

This shows that the equation that has x = -6 as solution is  $log_3(-2x-3)=2$. Option D is correct

Logarithm and exponents

Logarithm are inverse of exponential functions. According to the question, we are to determine the logarithm function that has a solution of x = -6

For the first option

$log_x36=2$

The exponential form of the result will be:

$x^{2}=36\\x^{2}=6^2\\x=6$

This shows that the expression is incorrect.

For the log expression $log_3(-2x-3)=2$

Simplify

$3^{2}=-2x-3\\2x=-9-3\\2x=-12\\x=-6$

This shows that the equation that has x = -6 as solution is  $log_3(-2x-3)=2$

Learn more on logarithm here: https://brainly.com/question/25710806

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