## anonymous 5 years ago 5^log(base x)5 = x^3

1. anonymous

first, by definition of logarithms, this is the same as writing $\log_x(5) = \log_5(x^3)$ From here, we can use the fact that $\log_b(a) = \frac{\ln(a)}{\ln(b)}$ to simplify: $\frac{\ln(5)}{\ln(x)} = \frac{\ln(x^3)}{\ln(5)}$ From here, you just need to solve for x.

2. anonymous

which i would multiply both 5's, and have it like so:

3. anonymous

$\ln(5)*\ln(5)/lnx*lnx^3$

4. anonymous

is that right?

5. anonymous

Do you mean $\ln(5)^2 = \ln(x)*\ln(x^3)$? Then, remember that $ln(x^3)$ is the same thing as $3*\ln(x)$, so we have $\ln(5)^2 = 3\ln(x)^2$ and from there solving should be simple.

6. anonymous

can you get on http://www.twiddla.com/503175 and explain please?