Question

5^log(base x)5 = x^3

Answer 1

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.

Answer 2

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

Answer 3

\[\ln(5)*\ln(5)/lnx*lnx^3\]

Answer 4

is that right?

Answer 5

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.

Answer 6

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