What is log_{10}((sqrt(a+2))/(\sqrt[3]{a+3)}) ?

The solution to log_{10}((sqrt(a+2))/(\sqrt[3]{a+3)}) is log_{10}(sqrt(a+2))-log_{10}(\sqrt[3]{a+3})

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simplify log_{10}((sqrt(a+2))/(\sqrt[3]{a+3)})

simplify

Solution steps

Apply log rule:

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

ln (3) - ln (\frac{1}{3})

ln (x) - 2 [ln (x - 7) + ln (x + 7)]

4 lo g_{b} (x) + \frac{1}{2} lo g_{b} (y) - 3 lo g_{b} (2 z)

lo g_{a} (\frac{3 ^{4}}{4 ^{2} a ^{7}})

ln (x^{\frac{1}{2}} y^{9}) - ln (z^{4})

What is log_{10}((sqrt(a+2))/(\sqrt[3]{a+3)}) ?
The solution to log_{10}((sqrt(a+2))/(\sqrt[3]{a+3)}) is log_{10}(sqrt(a+2))-log_{10}(\sqrt[3]{a+3})