# Math Help - Logarithmic expressions

1. ## Logarithmic expressions

Hi, I need help with the following question in the attachment. It is about logs, I don't understand this problem. Please help, thanks in advanced

2. ## Re: Logarithmic expressions

Note that $\log_8 {64} = 2$. Also, $\log_8 {64} = 3 \log_8 {4}$ by a logarithmic identity. Therefore

$3 \log_8 {4} = 2 \Rightarrow \log_8 {4} = \frac{2}{3}$.

3. ## Re: Logarithmic expressions

There is no exponent 3 though. How did you end up with log64 base 8?

4. ## Re: Logarithmic expressions

I'm using 64 because $64 = 4^3 = 8^2$.

5. ## Re: Logarithmic expressions

Originally Posted by dan713
Hi, I need help with the following question in the attachment. It is about logs, I don't understand this problem. Please help, thanks in advanced
Here is another way to look at it.
$x = {\log _8}(4)\; \Rightarrow {8^x} = 4\; \Rightarrow \;x = \frac{2}{3}$.

6. ## Re: Logarithmic expressions

Originally Posted by Plato
Here is another way to look at it.
$x = {\log _8}(4)\; \Rightarrow {8^x} = 4\; \Rightarrow \;x = \frac{2}{3}$.
That is correct but it might not be immediately apparent to dan713 that x = 2/3. Unless you note that $\sqrt[3]{8^2} = 4$, or you write it as $2^{3x} = 2^2$.