Answer :
5^x=1/125
Take log of both sides
log(5^x)=log(1/125)
x*(log(5))= log(1/125)
x= log(1/125)/ log(25)
x=-3
9^x= 243
Take log of both sides
log(9^x)= log(243)
x*(log(9))= log(243)
x= log(243)/ log(9)
x= 2.5
4^x= 1/32
Take log of
log(4^x)=log(1/32)
x*(log(4))=log(1/32)
x= log(1/32)/log(4)
x= -2.5
3*2^x=96
Divide both sides by 3 so we can make it more simply
3(2^x)/3= 96/3
2^x= 32
Take log of
log(2^X)=log(32)
x(log(2))= log(32)
x= log(32)/log(2)
x=5
As you can see, I only used a simple way for all of them.
I hope that's help:0
remember
if x^m=x^n and x=x, m=n
also
x^-m=1/(x^m)
(x^m)^n=x^(mn)
try to match bases
5^x=3125
5^x=5^5
x=5
5^x=1/125
1/125=1/(5^3)=5^-3
5^x=5^-3
x=-3
9^x=234
3^(2x)=3^5
2x=5
x=2.5
4^x=1/32
1/32=1/(2^5)=2^-5
2^(2x)=2^-5
2x=-5
x=-2.5
3*2^x=96
first divide both sides by 3
2^x=32
2^x=2^5
x=5
5^x=3125
x=5
5^x=1/125
x=-3
9^x=234
x=2.5
4^x=1/32
x=-2.5
3*2^x=96
x=5
if x^m=x^n and x=x, m=n
also
x^-m=1/(x^m)
(x^m)^n=x^(mn)
try to match bases
5^x=3125
5^x=5^5
x=5
5^x=1/125
1/125=1/(5^3)=5^-3
5^x=5^-3
x=-3
9^x=234
3^(2x)=3^5
2x=5
x=2.5
4^x=1/32
1/32=1/(2^5)=2^-5
2^(2x)=2^-5
2x=-5
x=-2.5
3*2^x=96
first divide both sides by 3
2^x=32
2^x=2^5
x=5
5^x=3125
x=5
5^x=1/125
x=-3
9^x=234
x=2.5
4^x=1/32
x=-2.5
3*2^x=96
x=5
