Solving for x in 3^(log(base4)x)

[turutk]

Homework Statement

integrate 3^(log(base4)x)

Homework Equations

The Attempt at a Solution

i tried to write it in different ways. couldn't solve.
i tried to divide the whole thing by ln3 and then add some more constants to cancel out the remainings. still i could not cancel out the x in the denominator which comes from the chain rule.

 

[micromass]

First, change the base of the log to base 3, using the correct formula.
Then apply the formula 3^{\log_3(x)}=x.

 

[turutk]

thank you very much for your help. at least i succeed

 

[dextercioby]

So you have to integrate

3^{x\ln 4}

Then you'll have to integrate

\left(e^{\ln 3}\right)^{x\ln 4}

which should be trivial, right ?

Unless you may have to integrate

3^\log_4 x

in which case you have to integrate

\left(e^{\ln 3}\right)^{\frac{\ln x}{\ln 4}}

which again should be trivial.