What is 2log_{10}(8)-3log_{10}(x) ?

The solution to 2log_{10}(8)-3log_{10}(x) is log_{10}((64)/(x^3))

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simplify 2log_{10}(8)-3log_{10}(x)

simplify

2 lo g_{10} (8) - 3 lo g_{10} (x)

lo g_{10} (\frac{64}{x ^{3}})

Solution steps

2 lo g_{10} (8) - 3 lo g_{10} (x)

2 lo g_{10} (8) = lo g_{10} (8^{2})

- 3 lo g_{10} (x) = - lo g_{10} (x^{3})

= lo g_{10} (8^{2}) - lo g_{10} (x^{3})

Apply log rule:

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

lo g_{10} (8^{2}) - lo g_{10} (x^{3}) = lo g_{10} (\frac{8 ^{2}}{x ^{3}})

= lo g_{10} (\frac{8 ^{2}}{x ^{3}})

Simplify

\frac{8 ^{2}}{x ^{3}} : \frac{64}{x ^{3}}

= lo g_{10} (\frac{64}{x ^{3}})

- \frac{ln ( 3 ) - ln ( 2 )}{ln ( 2 )}

\frac{1}{2} lo g_{10} (x) - 6 lo g_{10} (y)

lo g_{2} ((m + n) \cdot p)

lo g_{10} (\frac{x}{1000 y ^{8}})

lo g_{10} (\frac{u ^{2} + v ^{2}}{100})

What is 2log_{10}(8)-3log_{10}(x) ?
The solution to 2log_{10}(8)-3log_{10}(x) is log_{10}((64)/(x^3))