What is log_{30}(64)+log_{30}(15^3)-3log_{30}(2) ?

The solution to log_{30}(64)+log_{30}(15^3)-3log_{30}(2) is 6log_{30}(2)+log_{30}(3375/8)

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simplify log_{30}(64)+log_{30}(15^3)-3log_{30}(2)

simplify

lo g_{30} (64) + lo g_{30} (1 5^{3}) - 3 lo g_{30} (2)

6 lo g_{30} (2) + lo g_{30} (\frac{3375}{8})

Decimal

3

Solution steps

lo g_{30} (64) + lo g_{30} (1 5^{3}) - 3 lo g_{30} (2)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 lo g_{30} (2) = lo g_{30} (2^{3})

= lo g_{30} (64) + lo g_{30} (1 5^{3}) - lo g_{30} (2^{3})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{30} (1 5^{3}) - lo g_{30} (2^{3}) = lo g_{30} (\frac{1 5 ^{3}}{2 ^{3}})

= lo g_{30} (64) + lo g_{30} (\frac{1 5 ^{3}}{2 ^{3}})

\frac{1 5 ^{3}}{2 ^{3}} = \frac{3375}{8}

= lo g_{30} (64) + lo g_{30} (\frac{3375}{8})

lo g_{30} (64) = 6 lo g_{30} (2)

= 6 lo g_{30} (2) + lo g_{30} (\frac{3375}{8})

2 lo g_{10} (x) + lo g_{10} (11)

lo g_{10} (\frac{9 x ^{7} y}{x ^{2} y ^{4}})

2 lo g_{10} (0.1) + lo g_{10} (10) + lo g_{10} (0.001) - 5 lo g_{10} (0.0001)

lo g_{3} (13) + lo g_{3} (y)

\frac{1}{6} lo g_{2} (25) - \frac{1}{3} lo g_{2} (10)

What is log_{30}(64)+log_{30}(15^3)-3log_{30}(2) ?
The solution to log_{30}(64)+log_{30}(15^3)-3log_{30}(2) is 6log_{30}(2)+log_{30}(3375/8)