What is (log_{10}(9))/(log_{10)(4)} ?

The solution to (log_{10}(9))/(log_{10)(4)} is log_{2}(3)

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simplify (log_{10}(9))/(log_{10)(4)}

simplify

\frac{lo g _{10} ( 9 )}{lo g _{10} ( 4 )}

lo g_{2} (3)

Decimal Notation

1.58496 \dots

Solution steps

\frac{lo g _{10} ( 9 )}{lo g _{10} ( 4 )}

lo g_{10} (9) = 2 lo g_{10} (3)

= \frac{2 lo g _{10} ( 3 )}{lo g _{10} ( 4 )}

Apply log rule:

\frac{lo g _{c} ( b )}{lo g _{c} ( a )} = lo g_{a} (b)

\frac{lo g _{10} ( 3 )}{lo g _{10} ( 4 )} = lo g_{4} (3)

= 2 lo g_{4} (3)

Factor the number:

4 = 2^{2}

= 2 lo g_{2^{2}} (3)

Apply log rule:

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

lo g_{2^{2}} (3) = \frac{1}{2} lo g_{2} (3)

= 2 \cdot \frac{1}{2} lo g_{2} (3)

2 \cdot \frac{1}{2} lo g_{2} (3) = lo g_{2} (3)

= lo g_{2} (3)

\frac{x ^{2} + x - 2}{x ^{2} + 2 x - 3}

2 x - \frac{x}{2}

e ln (1)

(4 k)^{3}

2 x + 6 y

What is (log_{10}(9))/(log_{10)(4)} ?
The solution to (log_{10}(9))/(log_{10)(4)} is log_{2}(3)