Question

How do you solve -3log5x=-6?

Answer 1

-3log5x = -6 would equal x = 25.

First, use the Power Rule: (log b x
`^(c)` = c log b x). Your problem should look like -log5 x³ = -6.
Second, multiply both sides by -1. Your problem should look like log5 x³ = 6. We removed the negative signs.
Third, use the Definition of Common Logarithms. ( b
`^(a)`= x if and only if logb(x) = a). Your problem should look like x³ = 5
`^(6)`.
Fourth, simplify 5
`^(6)` to 15625. Your problem should look like x³ = 15625.
Fifth, take the cube root of both sides. Your problem should look like x = 3√15625.
Sixth, calculate your problem to get x = 25 which is the answer.