What is log_{8}((9x^3)/(4y^2)) ?

The solution to log_{8}((9x^3)/(4y^2)) is 2log_{8}(3)+log_{2}(x)-(6log_{8}(y)+2)/3

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simplify log_{8}((9x^3)/(4y^2))

simplify

lo g_{8} (\frac{9 x ^{3}}{4 y ^{2}})

2 lo g_{8} (3) + lo g_{2} (x) - \frac{6 lo g _{8} ( y ) + 2}{3}

Solution steps

lo g_{8} (\frac{9 x ^{3}}{4 y ^{2}})

Apply log rule:

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

lo g_{8} (\frac{9 x ^{3}}{4 y ^{2}}) = lo g_{8} (9 x^{3}) - lo g_{8} (4 y^{2})

= lo g_{8} (9 x^{3}) - lo g_{8} (4 y^{2})

lo g_{8} (9 x^{3}) = 2 lo g_{8} (3) + lo g_{2} (x)

lo g_{8} (4 y^{2}) = \frac{6 lo g _{8} ( y ) + 2}{3}

= 2 lo g_{8} (3) + lo g_{2} (x) - \frac{6 lo g _{8} ( y ) + 2}{3}

4 lo g_{10} (7) + 4 lo g_{10} (x)

ln (\frac{10}{2})

ln (\frac{s + 1}{s - 1})

ln (\frac{0.05}{0.02})

lo g_{b} (z^{4} x)

What is log_{8}((9x^3)/(4y^2)) ?
The solution to log_{8}((9x^3)/(4y^2)) is 2log_{8}(3)+log_{2}(x)-(6log_{8}(y)+2)/3