Question

How do you solve `5^x + 4(5^(x+1)) = 63`?

Answer 1

`x=log_5(3)`

Explanation:

Given:
`color(white)("XXX")5^x+4(5^(x+1))=63`

Extract the common factor of `5^x` from both terms on the left side:
`color(white)("XXX")5^x(1+4(5^1))=63`
Simplify the numeric expression
`color(white)("XXX")5^x(21)=63`
Divide both sides by `21`
`color(white)("XXX")5^x=3`
Apply the equivalence: `log_b a =c hArr b^c=a`
`color(white)("XXX")x=log_5(3)`