Question

Don't really know how to solve with log on this one. 3 * 5^(2x-1) = 75

Answer 1

\(3*5^{2x-1}=75\implies5^{2x-1}=25=5^2\)
taking log base 5 of both sides
\(\log_5(5^{2x-1})=\log_5(5^2)\implies 2x-1=2\)

Answer 2

\(\log_a(a^b)=b\log_a(a)=b*1=b\)

Answer 3

ok. thank u!

Answer 4

and how would I solve 5^(x+6)=7?

Answer 5

(x+6) * log(5) = log(7)
(x + 6) * 0.69897000434 = 0.84509804001
0.69897000434 x + 6*0.69897000434 = 0.84509804001
0.69897000434 x = 0.84509804001 - 4.193820026
0.69897000434 x = -3.34872198599
x = -4.79093804486

Answer 6

\(5^{x+6}=7\\\log_5(5^{x+6})=\log_5(7)\\x+6=\log_5(7)\\x=\log_5(7)-6\approx -4.790938.....\)

Answer 7

but never approximate, unless asked.

Answer 8

and DEFINITELY never approximate while doing the problem, only at the end...we are not physicist.

*cough* @wolf1728

Answer 9

That's the way I learned logarithms and it looks as though we got the same answer.

Answer 10

we have the same approximate:)

Answer 11

Yes but I carried out my answer to 5 more decimal places than you. So, who is the approximator now??
(just kidding)