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

The solution to 4log_{b}(2)+log_{b}(5) is log_{b}(80)

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

simplify

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

lo g_{b} (80)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

2^{4} \cdot 5 = 80

= lo g_{b} (80)

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

ln (\frac{8}{5 x ^{5} y})

lo g_{3} (\frac{6 y}{z})

ln (\frac{e ^{6}}{7})

\frac{1}{3} lo g_{b} (x^{4} y^{5}) - \frac{3}{4} lo g_{b} (x^{2} y)

What is 4log_{b}(2)+log_{b}(5) ?
The solution to 4log_{b}(2)+log_{b}(5) is log_{b}(80)