What is 1/2 log_{6}(9)+log_{6}(5) ?

The solution to 1/2 log_{6}(9)+log_{6}(5) is log_{6}(15)

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simplify 1/2 log_{6}(9)+log_{6}(5)

simplify

\frac{1}{2} lo g_{6} (9) + lo g_{6} (5)

lo g_{6} (15)

Decimal Notation

1.51139 \dots

Solution steps

\frac{1}{2} lo g_{6} (9) + lo g_{6} (5)

Apply log rule:

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

\frac{1}{2} lo g_{6} (9) = lo g_{6} (9^{\frac{1}{2}})

= lo g_{6} (9^{\frac{1}{2}}) + lo g_{6} (5)

Apply log rule:

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

lo g_{6} (9^{\frac{1}{2}}) + lo g_{6} (5) = lo g_{6} (9^{\frac{1}{2}} \cdot 5)

= lo g_{6} (9^{\frac{1}{2}} \cdot 5)

9^{\frac{1}{2}} \cdot 5 = 15

= lo g_{6} (15)

2 lo g_{b} (y) + 6 lo g_{b} (z)

ln^{2} (x) - ln (x)

ln (x) - 4 [ln (x + 2) + ln (x - 2)]

2 lo g_{b} (a) + 3 lo g_{b} (c^{2}) - 4 lo g_{b} (d)

lo g_{4} (a^{3} b^{3} \cdot c)

What is 1/2 log_{6}(9)+log_{6}(5) ?
The solution to 1/2 log_{6}(9)+log_{6}(5) is log_{6}(15)