Question

Help with simplifying logs!!

Answer 1

If the \[\log_b x = 0\] that means that \(b^0 = x\)

Looking at our problem from the outside in, if the log base 5 of the inner expression = 0, that means the inner expression = 5^0. What is 5^0?

Answer 2

1

Answer 3

Okay, so now we know that \(\log_3 x = 1\). That means that \(3^1 = x\) because the definition of the log tells us that the base^log = x. What is the value of x?

Answer 4

1?

Answer 5

Does 3^1 = 1?

Answer 6

no 3^0=1 .. so x=0?

Answer 7

No, we know that 3^1 = x. What is 3^1?

Answer 8

If \(3^0 = 1\), \(3^1 = 3*3^0 = 3*1 = 3\) right?

Answer 9

The \(\log_3 3 = 1\) because the base (3) to the power 1 = 3.

Answer 10

This problem is a little confusing because the same number is used for x and the base. Let's look at a similar one where that doesn't happen:

\[\log_3(\log_2 x)) = 2\]
If the \(\log_3 y = 2, \text{ }y = 3^2 = 9\) so our equation becomes
\[\log_2 x = 3^2 = 9\]If \(\log_2 x = 9, \text{ }x = 2^9 = 512\)

So \(\log_3(\log_2 (512)) = \log_3 (9) = 2\)