What is 3log_{a}(b)-1/2 log_{a}(c) ?

The solution to 3log_{a}(b)-1/2 log_{a}(c) is log_{a}((b^3sqrt(c))/c)

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simplify 3log_{a}(b)-1/2 log_{a}(c)

simplify

3 lo g_{a} (b) - \frac{1}{2} lo g_{a} (c)

lo g_{a} (\frac{b ^{3} c}{c})

Solution steps

3 lo g_{a} (b) - \frac{1}{2} lo g_{a} (c)

Apply log rule:

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

3 lo g_{a} (b) = lo g_{a} (b^{3})

= lo g_{a} (b^{3}) - \frac{1}{2} lo g_{a} (c)

Apply log rule:

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

\frac{1}{2} lo g_{a} (c) = lo g_{a} (c^{\frac{1}{2}})

= lo g_{a} (b^{3}) - lo g_{a} (c^{\frac{1}{2}})

Apply log rule:

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

lo g_{a} (b^{3}) - lo g_{a} (c^{\frac{1}{2}}) = lo g_{a} (\frac{b ^{3}}{c ^{\frac{1}{2}}})

= lo g_{a} (\frac{b ^{3}}{c ^{\frac{1}{2}}})

Simplify

\frac{b ^{3}}{c ^{\frac{1}{2}}} : \frac{b ^{3} c}{c}

= lo g_{a} (\frac{b ^{3} c}{c})

ln (15) - ln (5)

\frac{1}{4} lo g_{b} (x) + 5 lo g_{b} (y) - 4 lo g_{b} (x)

lo g_{10} (\frac{x}{100 y ^{8}})

lo g_{b} (x yz)

3 ln (x) + 6 ln (y) - 4 ln (z)

What is 3log_{a}(b)-1/2 log_{a}(c) ?
The solution to 3log_{a}(b)-1/2 log_{a}(c) is log_{a}((b^3sqrt(c))/c)