Asked by JB

2^(3x + 1) = 3^(x − 2)
(a) Find the exact solution of the exponential equation in terms of logarithms.
Answered by Reiny
take logs of both sides and use log rules
(3x+1)log2 = (x-2)log3
3log2 x + log2 = log3 x - 2log3
x(3log2 - log3) = -2log3 - lo2
x = (2log3 + log2)/(log3 - 3log2)
Answered by John
2 log(3x+1) = 3 log(x-2)

Get this step by using the law of logs regarding exponents.

log(3x +1) /log (x-2) = 3/2

log (3x + 1 -x +2) = 3/2
log (2x + 3) = 3/2

can you finish from here?



Answered by Reiny
John, you misread the question

2^(3x + 1) = 3^(x − 2)
is not the same as
2 log(3x+1) = 3 log(x-2)

then, log(3x +1) /log (x-2) ≠ log (3x + 1 -x +2)
e.g. is log100/log10 = log(100-10) ???
LS = 2/1 = 2
RS = log 90
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