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Popular >

simplify log_{125}(625)

Solution

simplify

lo g_{125} (625)

Solution

\frac{4}{3}

+1

Decimal Notation

1.33333 \dots

Solution steps

lo g_{125} (625)

Factor the number:

125 = 5^{3}

= lo g_{5^{3}} (625)

Apply log rule:

lo g_{a^{b}} (x) = \frac{1}{b} lo g_{a} (x), a > 0

lo g_{5^{3}} (625) = \frac{1}{3} lo g_{5} (625)

= \frac{1}{3} lo g_{5} (625)

Factor the number:

625 = 5^{4}

= \frac{1}{3} lo g_{5} (5^{4})

Apply log rule:

lo g_{a} (a^{b}) = b

lo g_{5} (5^{4}) = 4

= \frac{1}{3} \cdot 4

\frac{1}{3} \cdot 4 = \frac{4}{3}

= \frac{4}{3}

Popular Examples

∣ u ∣ > 3

simplify 3/10+3/15 simplify

\frac{3}{10} + \frac{3}{15}

12 s = 72

x^{2} - 11 x + 19 = 0

(5 \cdot 2 \cdot 3)^{4}

Frequently Asked Questions (FAQ)

What is log_{125}(625) ?
The solution to log_{125}(625) is 4/3