What is log_{b}(80)-log_{b}(5) ?

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

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simplify log_{b}(80)-log_{b}(5)

simplify

lo g_{b} (80) - lo g_{b} (5)

4 lo g_{b} (2)

Solution steps

lo g_{b} (80) - lo g_{b} (5)

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{b} (80) - lo g_{b} (5) = lo g_{b} (\frac{80}{5})

= lo g_{b} (\frac{80}{5})

Divide the numbers:

\frac{80}{5} = 16

= lo g_{b} (16)

Factor the number:

16 = 2^{4}

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

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

= 4 lo g_{b} (2)

ln (\frac{e ^{5}}{14})

lo g_{b} (\frac{x ^{2} y}{z ^{4}})

lo g_{b} (\frac{9}{8})

ln (x^{2} - 7) - ln (x + 6) - 3

lo g_{5} (x - 2) + lo g_{5} (3 x + 7)

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