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

The solution to log_{4}(2)+2log_{4}(5) is log_{4}(50)

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

simplify

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

lo g_{4} (50)

Decimal Notation

2.82192 \dots

Solution steps

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

Apply log rule:

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

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

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

2 \cdot 5^{2} = 50

= lo g_{4} (50)

ln (\frac{s ^{2} + 1}{( s - 1 ) ^{2}})

ln (9) + ln (x) + ln (y)

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

ln (x) + ln (x + 2)

lo g_{2} (7 x)

What is log_{4}(2)+2log_{4}(5) ?
The solution to log_{4}(2)+2log_{4}(5) is log_{4}(50)