Question 1148576

Hello, this is a logarithmic problem. I need a step by step explanation of:
16^log4(8). I know the answer is 64, but I need to show my work.
Is it possible to solve this problem by rewriting 16 as 2^4 and log 4 as 2^2 and 8 as 2^3. If so, please explain
<pre>It is longer, but yes, it can be done!
{{{16^log (4, (8))}}}
{{{log (4, (8))}}} can be written as: {{{log (2^2, (2^3))}}}, which means that: {{{matrix(1,3, (2^2)^x, "=", (2)^3)}}}, which becomes: {{{matrix(1,3, 2^(2x), "=", 2^3)}}}
Now, 2x = 3, since the BASES are equal, and so, {{{matrix(1,3, x, "=", 3/2)}}}
We now see that: {{{highlight(highlight_green(highlight(matrix(1,11, 16^(log (4, (8))), "becomes:", matrix(2,1, " ", 16^(3/2)),
"=====>", (2^4)^(3/2),
"=====>", 2^(4 * (3/2)),
"====>", 2^6, "=", 64)))))}}}