## Practice questions

- If 3
= 4^{x}and 5^{y}= 6^{y}, then^{z} - For which of following values for
*x*is log_{6}4 + log_{6}*x*= 2?

## Answers and explanations

- The correct answer is Choice
**(B).**Looking at the answer choices tells you you're dealing with a logarithm problem. Because you're solving for

and none of the answers has a

*y*variable, you need to get rid of the*y*variables in the original equations. You can do this by solving both equations for*y*and them setting them equal to each other. Then, you can manipulate the equation to solve forFirst, take the log of both sides of the first equation and solve for

*y*:Then, take the log of both sides of the other equation and solve for

*y*:Set the equations equal to each other and move terms around until you've solved for

*x*/*z*: - The correct answer is Choice
**(D).**When you add logs with the same base, you solve by multiplying: log

_{6}(4*x*) = 2.Then you can plug in the options for

*x*. Choice (D) is correct. The product of 4 and 9 is 36, which is the value you get when you multiply 6 by itself two times.Choice (E) incorrectly adds 4 and

*x*.