What is 2log_{b}(2)-log_{b}(7)-4log_{b}(5) ?

The solution to 2log_{b}(2)-log_{b}(7)-4log_{b}(5) is log_{b}(4/4375)

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simplify 2log_{b}(2)-log_{b}(7)-4log_{b}(5)

simplify

2 lo g_{b} (2) - lo g_{b} (7) - 4 lo g_{b} (5)

lo g_{b} (\frac{4}{4375})

Solution steps

2 lo g_{b} (2) - lo g_{b} (7) - 4 lo g_{b} (5)

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

- 4 lo g_{b} (5) = - lo g_{b} (5^{4})

= lo g_{b} (2^{2}) - lo g_{b} (7) - lo g_{b} (5^{4})

Apply log rule:

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

lo g_{b} (2^{2}) - lo g_{b} (7) = lo g_{b} (\frac{2 ^{2}}{7})

= lo g_{b} (\frac{2 ^{2}}{7}) - lo g_{b} (5^{4})

Apply log rule:

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

lo g_{b} (\frac{2 ^{2}}{7}) - lo g_{b} (5^{4}) = lo g_{b} (\frac{\frac{2 ^{2}}{7}}{5 ^{4}})

= lo g_{b} (\frac{\frac{2 ^{2}}{7}}{5 ^{4}})

\frac{\frac{2 ^{2}}{7}}{5 ^{4}} = \frac{4}{4375}

= lo g_{b} (\frac{4}{4375})

lo g_{10} (30) - lo g_{10} (5)

lo g_{5} (25 (x^{2} - 49))

4 ln (x) + ln (3) - ln (x)

lo g_{9} (z x \cdot y)

lo g_{4} (10000 x)

What is 2log_{b}(2)-log_{b}(7)-4log_{b}(5) ?
The solution to 2log_{b}(2)-log_{b}(7)-4log_{b}(5) is log_{b}(4/4375)