What is 4log_{10}(r)-log_{10}(x) ?

The solution to 4log_{10}(r)-log_{10}(x) is log_{10}((r^4)/x)

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simplify 4log_{10}(r)-log_{10}(x)

simplify

4 lo g_{10} (r) - lo g_{10} (x)

lo g_{10} (\frac{r ^{4}}{x})

Solution steps

4 lo g_{10} (r) - lo g_{10} (x)

Apply log rule:

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

4 lo g_{10} (r) = lo g_{10} (r^{4})

= lo g_{10} (r^{4}) - lo g_{10} (x)

Apply log rule:

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

lo g_{10} (r^{4}) - lo g_{10} (x) = lo g_{10} (\frac{r ^{4}}{x})

= lo g_{10} (\frac{r ^{4}}{x})

\frac{3}{4} ln (x) + \frac{1}{4} ln (y)

lo g_{10} (x^{3}) y^{2}

lo g_{10} (\frac{1}{a})

\frac{2}{3} lo g_{3} (2 x - 5) - 5 lo g_{3} (4 x + 2)

- \frac{ln ( 2 )}{5 ln ( 3 )}

What is 4log_{10}(r)-log_{10}(x) ?
The solution to 4log_{10}(r)-log_{10}(x) is log_{10}((r^4)/x)