SOLUTION: Find all real solutions to the equations, please explain how: 4log_5(8-x)=7 and 12(4^(3x))=120 Thank you

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Question 951923: Find all real solutions to the equations, please explain how:
4log_5(8-x)=7
and
12(4^(3x))=120
Thank you
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
The form of each is very similar.

k%2Alog%28b%2CX%29=r

log%28b%2CX%29=r%2Fk

b%5E%28r%2Fk%29=X
possible other adjustments if X is an expression.


4%2Alog%285%2C%28%288-x%29%29%29=7, but you might want to use Change Of Base formula.
Ignoring that for now,
log%285%2C%28%288-x%29%29%29=7%2F4
(the rendering is not working too well for display)
5%5E%287%2F4%29=8-x
-5%5E%287%2F4%29=-8%2Bx
x=8-5%5E%287%2F4%29
You might want to use table of logarithms to handle that second term on the right,... or just use calculator.

x=-8.7185....