5^(4-x)=1/5 Process for solving

[Monocerotis]

Homework Statement

5^4-x = 1/5

How would I go about solving a problem like this up until now I haven't had to deal with fractions on either side of an equation

Homework Equations

The Attempt at a Solution

 

[Mark44]

You can rewrite this as 5^{4 - x} = 5^-1.

You can use the idea that if a^x = a^y, then x = y.

 

[Architeuthis Dux]

To solve this equation, first multiply both sides by 5 to get rid of the fraction:

5^(4-x) = 1/5
5^(4-x) * 5 = 1/5 * 5
5^(4-x+1) = 1
5^(5-x) = 1

Next, we can rewrite the left side using exponent rules:

5^(5-x) = 1
5^(5) / 5^x = 1
5^5 = 5^x

Now, we can solve for x by taking the logarithm of both sides with base 5:

log5(5^5) = log5(5^x)
5 = x

Therefore, the solution to the original equation is x = 5.