What is (log_{10}(asqrt(c))+2log_{10}(b))/4 ?

The solution to (log_{10}(asqrt(c))+2log_{10}(b))/4 is (log_{10}(asqrt(c)b^2))/4

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simplify (log_{10}(asqrt(c))+2log_{10}(b))/4

simplify

\frac{lo g _{10} ( a c ) + 2 lo g _{10} ( b )}{4}

\frac{lo g _{10} ( a c b ^{2} )}{4}

Solution steps

\frac{lo g _{10} ( a c ) + 2 lo g _{10} ( b )}{4}

Apply log rule:

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

2 lo g_{10} (b) = lo g_{10} (b^{2})

= \frac{lo g _{10} ( a c ) + lo g _{10} ( b ^{2} )}{4}

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{10} (a c) + lo g_{10} (b^{2}) = lo g_{10} (a b^{2} c)

= \frac{lo g _{10} ( a c b ^{2} )}{4}

ln (\frac{e ^{2 y} x y}{x ^{3}})

\frac{1}{2} ln (\frac{y - 3}{x + 2})

4 ln (2) - 4 ln (2 x)

ln (3) + ln (2) ln (6)

4 ln (x) + 2 ln (y) - 10

What is (log_{10}(asqrt(c))+2log_{10}(b))/4 ?
The solution to (log_{10}(asqrt(c))+2log_{10}(b))/4 is (log_{10}(asqrt(c)b^2))/4