Question

Please help! Solve for x: x=log_4 5.
An intermediate step is?

Answer 1

Is this the entire question?
Cause I know how to work this question, the question just isn't complete.

Answer 2

log_4 (5) is a numerical value, and x = log_4 (5) , there's nothing to solve, unless you want to find the exact value, use a calculator :)

Answer 3

\[x=\log_{4} 5\]
\[4^{x}=5\]
\[x \ln 4=\ln 5\]
\[x=\frac{\ln 5}{\ln 4}\]

Answer 4

@Johnjakile1998 Yea, it's the complete question. It's just asking for an intermediate step when solving :/ Thank you @sasogeek and @kropot72 :)

Answer 5

So, do you still need help?

Answer 6

You're welcome :)

Answer 7

what @kropot72 did was show how to get x in terms of natural log
most calculators only have natural log or log base 10

the short version is known as change of base formula
\[\log_{b}A = \frac{\ln A}{\ln b} = \frac{\log A}{\log b} \]

Answer 8

the natural log is just log to the base e. truth is, log to any base will do, but it's best if we stick to the standards, just saying :) and here's what i'm saying :P

\(\huge log_bA=\frac{log_{10}A}{log_{10}b}=\frac{log_{5}A}{log_{5}b}=\frac{lnA}{lnb}=\frac{log_{23}A}{log_{23}b} \)
and so on and so forth :)

Answer 9

Thank you @dumbcow Sorry, OS keeps lagging on me :(

Answer 10

So we can say
\[\log_{b} A=\frac {\log_{} A}{\log_{} b}\]