What is 1/2 log_{4}(25)+log_{4}(2) ?

The solution to 1/2 log_{4}(25)+log_{4}(2) is log_{4}(10)

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simplify 1/2 log_{4}(25)+log_{4}(2)

simplify

\frac{1}{2} lo g_{4} (25) + lo g_{4} (2)

lo g_{4} (10)

Decimal Notation

1.66096 \dots

Solution steps

\frac{1}{2} lo g_{4} (25) + lo g_{4} (2)

Apply log rule:

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

\frac{1}{2} lo g_{4} (25) = lo g_{4} (2 5^{\frac{1}{2}})

= lo g_{4} (2 5^{\frac{1}{2}}) + lo g_{4} (2)

Apply log rule:

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

lo g_{4} (2 5^{\frac{1}{2}}) + lo g_{4} (2) = lo g_{4} (2 5^{\frac{1}{2}} \cdot 2)

= lo g_{4} (2 5^{\frac{1}{2}} \cdot 2)

2 5^{\frac{1}{2}} \cdot 2 = 10

= lo g_{4} (10)

- \frac{2}{3} lo g_{b} (x + 1) - \frac{1}{4} lo g_{b} (x + 2)

ln (\frac{e ^{8 x} + 1}{e ^{- 3 x} + 1})

- \frac{6}{9} lo g_{2} (\frac{6}{9}) - \frac{3}{9} lo g_{2} (\frac{3}{9})

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

lo g_{7} (2) + lo g_{7} (5)

What is 1/2 log_{4}(25)+log_{4}(2) ?
The solution to 1/2 log_{4}(25)+log_{4}(2) is log_{4}(10)