Question

What is 5^(2x-2) = 35??

Answer 1

Well Distribute the 5 and tell me what you get

Answer 2

x = (3 log(5)+log(7))/(2 log(5))
?

Answer 3

Wow I got no clue

Answer 4

use this property
\[\log(a^b)= b \log(a)\]

so your equation becomes
(2x-2)log(5) = log(35)
or
\[ 2x-2= \frac{log(35)}{log(5} \]
\[ x= \frac{log(35)}{2log(5)} +1\]

you can massage this into all kinds of things using these rules:
log(a b)= log(a)+log(b)
and the exponent rule.
for example 35= 5 x 7 so log(35)= log(5*7)= log(5)+log(7)

so you could get
\[ x= \frac{log(5)+log(7)}{2log(5)} +\frac{2log(5)}{2log(5)} = \frac{3log(5)+log(7)}{2log(5)} \]

or using 2log(5)= log(5^2)= log(25)
\[ x= \frac{log(5*25*7)}{log(25)}= \frac{log(875)}{log(25)} \]