Question

Logarithms

3^x-2=18
Work
log(3^x-2)=log18
(x-2)log3=log18
xlog3-2log3=log18
x=log3/(log9-log18)

e^3x+1=10
lne^3x+1=ln10
3x+1=ln10
I'm stuck here

8^x=5^2x-1
xlog8=(2x-1)log5
xlog8=2xlog5-log5
x=log10/(log5-log8)

Are these right?

Answer 1

humm
3^(x-2) = 18 ? = 2 * 9

3^(x-2) = 2 * 3^2

2 = 3^(x-4)

log 2 = (x-4) log 3

================
e^(3x+1) = 10 ?
3x + 1 = ln 10
3x = ln 10 - 1
x = (1/3)ln 10 - 1/3
======================
xlog 8 = x log 2^3 = 3 x log 2
3 x log 2 = 2 x log 5 - log 5
log 5 = x (2 log 5 -3 log 2)
x = log 5/(2 log 5 -3 log 2)