Question

How do you calculate `log_(1/625) 125`?

Answer 1

`log_(1/625)(125)= -3/4`

Explanation:

We will use the following:

• `y = log_a(x) <=> a^y = x` (for `x>0`)
• `log_a(a^x) = x`
• `(a^b)^c = a^(bc)`
• `a^(-b) = 1/a^b`

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Let `x = log_(1/625)(125)`

`=> (1/625)^x = 125`

`=> (5^(-4))^x = 5^3`

`=> 5^(-4x) = 5^3`

`=> log_5(5^(-4x)) = log_5(5^3)`

`=> -4x = 3`

`:. x = -3/4`