What is 1/3*log_{4}(8)+log_{4}(15) ?

The solution to 1/3*log_{4}(8)+log_{4}(15) is log_{4}(30)

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simplify 1/3*log_{4}(8)+log_{4}(15)

simplify

\frac{1}{3} \cdot lo g_{4} (8) + lo g_{4} (15)

lo g_{4} (30)

Decimal Notation

2.45344 \dots

Solution steps

\frac{1}{3} lo g_{4} (8) + lo g_{4} (15)

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

\frac{1}{3} lo g_{4} (8) = lo g_{4} (8^{\frac{1}{3}})

= lo g_{4} (8^{\frac{1}{3}}) + lo g_{4} (15)

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{4} (8^{\frac{1}{3}}) + lo g_{4} (15) = lo g_{4} (8^{\frac{1}{3}} \cdot 15)

= lo g_{4} (8^{\frac{1}{3}} \cdot 15)

8^{\frac{1}{3}} \cdot 15 = 30

= lo g_{4} (30)

2 lo g_{b} (x) + 7 lo g_{b} (z)

lo g_{4} (\frac{ab}{c d})

ln (x - 2) - ln (2 x - 3)

lo g_{10} (5 x) - 7 (10 x - 2)

ln (\frac{6 x}{x ^{2} - 4})

What is 1/3*log_{4}(8)+log_{4}(15) ?
The solution to 1/3*log_{4}(8)+log_{4}(15) is log_{4}(30)