Question

Which logarithmic equation is equivalent to 32 = 9?

2=log3(9)
2=log9(3)
3=log2(9)
3=log9(2)

Answer 1

To answer this problem, we should always remember that:

x^m = y

is equivalent to

logx(y) = m

Therefore using this formula in the given expression above where:

x = 3

m = 3

y = 9

Then,

log3(9) = 2

Answer: A

Answer 2

`2=log_3(9)`

Explanation:

The given exponential equation is

`3^2=9`

We take the logarithm of both sides to base 3 to obtain;

`log_3(3^2)=log_3(9)`

Recall that;

`log_a(a^n)=n\:log_a(a)=n`

We apply this property to the left hand side to obtain;

`2log_3(3)=log_3(9)`

`2(1)=log_3(9)`

This simplifies to

`2=log_3(9)`

The correct answer is option A