Solve 3^(4x-7)=4^(2x+3)

Question

anonymous · Answer

How? Can you tell me how you got to your answer?

anonymous · Answer

looks like you have a classmate that asked this question :-) http://openstudy.com/study#/updates/4f3d9363e4b0cf389e29a835

asnaseer · Answer

Take logs of both sides, specifically use this property of logs:$$\log(x^a)=a\log(x)$$

anonymous · Answer

Yes I do have a class mate who asked this question also, our teacher assigned us to do this. Thank you

anonymous · Answer

Lol :-)

anonymous · Answer

$$3^{4x-7}=4^{2x+3}$$
Taking log on both sides,
$$Log _{b}3^{4x-7}=Log _{b}4^{2x+3}$$
According to rule of exponents,
$$(4x-7)Log _{b}3=(2x+3)Log _{b}4$$
$$(4x-7)=(2x+3)Log _{b}4/Log _{b}3$$
$$(4x-7)/(2x+3)=Log _{b}4/Log _{b}3$$
$$2.52x+3.78=4x-7$$
$$3.78+7=4x-2.52x=1.48x$$
$$10.78=1.48x$$
$$10.78/1.48=x$$
$$7.28=x$$
Thats the answer I think o.o

anonymous · Answer

Thats incorrect but its close to the actual answer.

anonymous · Answer

@vengeance, you don't want to compute the logs until the very last step.  In physics, if you do that there's a teacher at my school who marks students off if the answer is even slightly off from theirs (not only do they require correct sig figs, but waiting until the very end to do the calculations like with logs,division, and square roots).

anonymous · Answer

The correct answer is 7.305

anonymous · Answer

@Ruse: Here, a difference of 0.02 in the answer doesn't make an enormous difference, but if you get the answer your way and you're satisfied with it...there's no problem absolutely. :)
@Brine: I see that in your school some teachers are more strict than the others. Still, in this case I couldn't find a better step to compute and calculate the log values other than the one I just did there, still if you know a better way to approach the question, please do tell me so I can learn it properly. Thanks!