SOLUTION: I need to solve the equation{{{4^(3x)=7^(x+1)}}}.My teacher uses handouts to teach,so I am stumped with no material to reference.Please help.Thanks.

Question 85515: I need to solve the equation.My teacher uses handouts to teach,so I am stumped with no material to reference.Please help.Thanks.
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
4^(3x)=7^(x+1)
Since the variables are in the exponent, take the log of both sides to get:
(3x)log4 = (x+1)log7
(3log4)x = (log7)x + log7
(3log4-log7)x = log7
log[(4^3)/7]x = log7
0.961081934x = 0.84509804
x=0.8793194525...
===========
Cheers,
Stan H.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Take the log (which has a default base of 10) of both sides

Rewrite the logarithms using the identity

Subtract from both sides

Distribute

Distribute the negative

Add

Factor out an x

Rewrite the logarithm using the identity

Raise 4 to the third power

Combine the logs using

Divide both sides by

Using and as approximations, evaluate the logs

Divide

Check:

Plug in

works

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