SOlve 13^4x = 7 for x. I got like a random negative decimal... what am i doing wrong?

Question

unklerhaukus · Answer

$$13^{4x}=7$$
is this your question/

unklerhaukus · Answer

or     $13^4x=7$

anonymous · Answer

the first one...

unklerhaukus · Answer

what answer did you get/

anonymous · Answer

i got -3.241345587040701

anonymous · Answer

Take the natural log of both sides:

13^4x = 7

ln13^4x = ln7

by the properties of logarithms, we can pull down the exponent 4x:

4x(ln13) = ln7

4x = ln7/ln13

x = 4(ln7/ln13)

anonymous · Answer

the answer should be about 3.03....

unklerhaukus · Answer

your method is good @Hermeezey
but in you last step you made a little mistake

$$4x = \frac{\ln7}{\ln13}$$
$$x=\frac{\ln7}{4\ln13}\approx3.03$$

unklerhaukus · Answer

i mean $x\approx0.1897$

anonymous · Answer

oh yea sorry, i get confused when i'm typing

anonymous · Answer

thanks :)

unklerhaukus · Answer

it is always good to check the solution by pluggin it into the original equation

$$13^{4\times0.1897}\approx13^{3/4}\approx6.8\approx7$$