What is log_{4}((x^2)/(y^2z^7)) ?

The solution to log_{4}((x^2)/(y^2z^7)) is log_{2}(x)-log_{2}(y)-7log_{4}(z)

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simplify log_{4}((x^2)/(y^2z^7))

simplify

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

lo g_{2} (x) - lo g_{2} (y) - 7 lo g_{4} (z)

Solution steps

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

Apply log rule:

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

lo g_{4} (\frac{x ^{2}}{y ^{2} z ^{7}}) = lo g_{4} (x^{2}) - lo g_{4} (y^{2} z^{7})

= lo g_{4} (x^{2}) - lo g_{4} (y^{2} z^{7})

lo g_{4} (x^{2}) = lo g_{2} (x)

lo g_{4} (y^{2} z^{7}) = lo g_{2} (y) + 7 lo g_{4} (z)

= lo g_{2} (x) - (lo g_{2} (y) + 7 lo g_{4} (z))

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{2} (y) + 7 lo g_{4} (z)) = - lo g_{2} (y) - 7 lo g_{4} (z)

= lo g_{2} (x) - lo g_{2} (y) - 7 lo g_{4} (z)

4 (ln (3) - ln (2)) + 6 (ln (7) - ln (6))

2 ln (\frac{α q}{α + 1})

lo g_{10} (\frac{x}{1000 y ^{3}})

\frac{1}{2} (- 5 lo g_{10} (x) + lo g_{10} (y z^{3}))

\frac{ln ( \frac{1034}{40353607} )}{2 ln ( 7 )}

What is log_{4}((x^2)/(y^2z^7)) ?
The solution to log_{4}((x^2)/(y^2z^7)) is log_{2}(x)-log_{2}(y)-7log_{4}(z)