What is log_{10}((y^4)/(100x)) ?

The solution to log_{10}((y^4)/(100x)) is 4log_{10}(y)-2-log_{10}(x)

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simplify log_{10}((y^4)/(100x))

simplify

lo g_{10} (\frac{y ^{4}}{100 x})

4 lo g_{10} (y) - 2 - lo g_{10} (x)

Solution steps

lo g_{10} (\frac{y ^{4}}{100 x})

Apply log rule:

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

lo g_{10} (\frac{y ^{4}}{100 x}) = lo g_{10} (y^{4}) - lo g_{10} (100 x)

= lo g_{10} (y^{4}) - lo g_{10} (100 x)

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

lo g_{10} (100 x) = 2 + lo g_{10} (x)

= 4 lo g_{10} (y) - (2 + lo g_{10} (x))

Apply the distributive law:

- (a + b) = - a - b

- (2 + lo g_{10} (x)) = - 2 - lo g_{10} (x)

= 4 lo g_{10} (y) - 2 - lo g_{10} (x)

lo g_{10} (\frac{x}{y ^{5}})

- \frac{3}{7} \cdot lo g_{2} (\frac{3}{7}) - \frac{4}{7} \cdot lo g_{2} (\frac{4}{7})

lo g_{10} (5) + lo g_{10} (8)

\frac{1}{4} ln (y) + ln (z)

What is log_{10}((y^4)/(100x)) ?
The solution to log_{10}((y^4)/(100x)) is 4log_{10}(y)-2-log_{10}(x)