SOLUTION: Solve for x in the following. A) 3^x=27 B) 16^x=64 C) 2=(1/32)^x D) 5^(x-4)=25^(2x+1)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve for x in the following. A) 3^x=27 B) 16^x=64 C) 2=(1/32)^x D) 5^(x-4)=25^(2x+1)      Log On


   

Question 1006392: Solve for x in the following.
A) 3^x=27
B) 16^x=64
C) 2=(1/32)^x
D) 5^(x-4)=25^(2x+1)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Solve for x in the following.
A)
3%5Ex=27
3%5Ex=3%5E3.......if base same, exponents are same too
x=3
or, using logarithm:
log%283%5Ex%29=log%2827%29
log%283%5Ex%29=log%283%5E3%29
x%2Alog%283%29=3%2Alog%283%29
x=3%2Alog%283%29%2Flog%283%29
x=3

B)
16%5Ex=64
%282%5E4%29%5Ex=2%5E6
2%5E%284x%29=2%5E6.........if base same, exponents are same too
4x=6
x=6%2F4
x=3%2F2
C)
2=%281%2F32%29%5Ex
2=1%5Ex%2F32%5Ex
2=1%2F32%5Ex
2%2A32%5Ex=1
2%2A%282%5E5%29%5Ex=1
2%2A2%5E%285x%29=1
2%5E%285x%2B1%29=1......since 1=2%5E0, we have
2%5E%285x%2B1%29=2%5E0......if base same, we have
5x%2B1=0
5x=-1
x=-1%2F5
D)
+5%5E%28x-4%29=25%5E%282x%2B1%29
+5%5E%28x-4%29=%285%5E2%29%5E%282x%2B1%29
+5%5E%28x-4%29=5%5E%282%282x%2B1%29%29
+5%5E%28x-4%29=5%5E%284x%2B2%29......if base same, we have
+x-4=4x%2B2
-2-4=4x-x
-6=3x
x=-6%2F3
x=-2

you can do it using logarithm like I did in A