What is log_{4}(6)+2log_{4}(5) ?

The solution to log_{4}(6)+2log_{4}(5) is log_{4}(150)

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simplify log_{4}(6)+2log_{4}(5)

simplify

lo g_{4} (6) + 2 lo g_{4} (5)

lo g_{4} (150)

Decimal Notation

3.61440 \dots

Solution steps

lo g_{4} (6) + 2 lo g_{4} (5)

Apply log rule:

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

2 lo g_{4} (5) = lo g_{4} (5^{2})

= lo g_{4} (6) + lo g_{4} (5^{2})

Apply log rule:

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

lo g_{4} (6) + lo g_{4} (5^{2}) = lo g_{4} (6 \cdot 5^{2})

= lo g_{4} (6 \cdot 5^{2})

6 \cdot 5^{2} = 150

= lo g_{4} (150)

lo g_{10} (10 x)

ln (x) + ln (9)

lo g_{b} (8 k)

- lo g_{10} (4 \cdot 1 0^{- 10})

lo g_{8} (6) + lo g_{8} (x)

What is log_{4}(6)+2log_{4}(5) ?
The solution to log_{4}(6)+2log_{4}(5) is log_{4}(150)