solve the equation 5^3x-2=(1/25)^x

Question

the 3x-2 is all one exponent

Answer 1

5^(3x-2)=(1/25)^x

5^(3x-2)=(5^(-2))^x

5^(3x-2)=5^(-2x)

(3x-2)=-2x

3x-2+2x=0

5x-2=0

5x=2

x=2/5

check:5^(3*(2/5)-2)=(1/25)^(2/5)

5^(6/5 - 2)=(5^-2)^(2/5)

5^(-4/5)=5^(-4/5)

Answer 2

You need to get both sides to have the same base, which is easy enough, given that 25 is 5².  Also remember that 1/something is that something raised to the negative power.

 

Rewrite the right side of your equation, so that you have the following:

 

5^3x-2 = (5^-2)x

 

5^3x-2 = 5^-2x

 

Now...if the bases are equal, the exponents must also be equal, and we can forget about the 5's and focus here:

 

3x-2 = -2x  This is easy enough to solve

5x=2

x = 2/5

 

 

Answer 3

2/5