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Help solving exponential equations?
I need help solving equations like the ones below. These are more complex than I have done before. Thanks for your help!!
9^x = 3/3^x
8^x = cube root(2/4^x)
20(1/2)^x/4 = 8
3 ln (x-3) + 4 = 5
1 Answer
- ?Lv 68 years agoFavorite Answer
Please note (a^m)^n=a^mn
so,9^x=3^2x
3^3x=3,3x=1,x=1/3
Double Check,9^(1/3)=3/3^1/3
2.080083823=3/1.44224957=2.080083823
=============================================
2^3x=(2/2^2x)^1/3=[2^(1-2x)]^1/3=2^(1/3 -2x/3)
3x=1/3 -2x/3
3 2/3 x=1/3
11x/3=1/3
x=1/3 /11/3=1/11
===========================
(1/2)^x/4=8/20=2/5
x/4=ln (2/5) /ln (1/2)=1.322
x=5.2877
==============================
3 ln (x-1)=1
ln (x-1)=1/3
x-1=e^(1/3)=20.0855
x=21.0855
God bless you.