Question

Tom is using logarithms to solve the equation 3^2x = 32. Which of the following equations would be equivalent to his original expression?
2x log 3 =log 32
3 log 2x =32
2 log 3 = x log 32
x log 3 =2 log 32

Answer 1

ANSWER

$2x \: log(3) = log(32)$

EXPLANATION

The given exponential equation is

${3}^{2x} = 32$

Tom is using logarithm to solve this question. Tom is expected to take logarithm of both sides of the exponential equation to a common base.

Let us say Tom took logarithm of both sides to base 10.

Then the equation becomes,

$log( {3}^{2x} ) = log(32)$

Tom needs to apply the following properties of logarithm :

$log( {a}^{n} ) =n \: log(a)$

to the left hand side to obtain,

$2x \: log(3) = log(32)$

The correct answer is A.

Answer 2

3^(2x)=32  so taking log of both sides

2x*log3=log32