What is log_{4}(8)+2log_{4}(5) ?

The solution to log_{4}(8)+2log_{4}(5) is log_{4}(200)

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simplify log_{4}(8)+2log_{4}(5)

simplify

lo g_{4} (8) + 2 lo g_{4} (5)

lo g_{4} (200)

Decimal Notation

3.82192 \dots

Solution steps

lo g_{4} (8) + 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} (8) + lo g_{4} (5^{2})

Apply log rule:

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

lo g_{4} (8) + lo g_{4} (5^{2}) = lo g_{4} (8 \cdot 5^{2})

= lo g_{4} (8 \cdot 5^{2})

8 \cdot 5^{2} = 200

= lo g_{4} (200)

lo g_{3} (\frac{3 x ^{5}}{y})

ln (a + b) + ln (a - b) - 6 ln (c)

lo g_{10} (2) + lo g_{10} (3) + lo g_{10} (4)

\frac{2}{3} ln (x) - \frac{1}{2} ln (y)

ln (\frac{1}{x ^{n}})

What is log_{4}(8)+2log_{4}(5) ?
The solution to log_{4}(8)+2log_{4}(5) is log_{4}(200)