1. ## Quick Question

Im working on a question and Im almost done but i cannot simplify it. So the question is 8 to the power of what equals 16? OR 8^X = 16

2. Originally Posted by Nikola
Im working on a question and Im almost done but i cannot simplify it. So the question is 8 to the power of what equals 16? OR 8^X = 16

Remember that $\displaystyle 8=2^3 \mbox{ and } 16=2^4$

so now we get

$\displaystyle \left( 2^3 \right)^x=2^4 \iff 2^{3x}=2^4$

Since the bases are equal the exponents must be equal. So we need to solve

$\displaystyle 3x=4 \iff x=\frac{4}{3}$

This problem could also be done using logs.

I hope this helps.

Good luck.

3. Hello !

Originally Posted by Nikola
Im working on a question and Im almost done but i cannot simplify it. So the question is 8 to the power of what equals 16? OR 8^X = 16

You can use the logarithms, or better :

$\displaystyle 8^x=16$

$\displaystyle 8=2^3$ and $\displaystyle 16=2^4$

---> $\displaystyle (2^3)^x=2^4$

$\displaystyle 2^{3x}=2^4$ (using the $\displaystyle (a^b)^c=a^{bc}$ rule)

So 3x=...

Edit : still too slcow !

4. Originally Posted by Moo
Hello !

You can use the logarithms....
$\displaystyle 8^x=16\rightarrow\log_8{16}=x$

$\displaystyle \log_8{16}=\frac{\log_{10}{16}}{\log_{10}{8}}=\fra c{\log{16}}{\log{8}}=\frac{4}{3}$