What is 2log_{10}(a)+2log_{10}(b) ?

The solution to 2log_{10}(a)+2log_{10}(b) is log_{10}(a^2b^2)

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simplify 2log_{10}(a)+2log_{10}(b)

simplify

2 lo g_{10} (a) + 2 lo g_{10} (b)

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

Solution steps

2 lo g_{10} (a) + 2 lo g_{10} (b)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{4} (17 x)

lo g_{3} (\frac{z}{27})

ln (3) + \frac{1}{3} ln (64)

lo g_{a} (\frac{x ^{2} y}{z ^{3}})

ln (\frac{x ^{6}}{y ^{5}})

What is 2log_{10}(a)+2log_{10}(b) ?
The solution to 2log_{10}(a)+2log_{10}(b) is log_{10}(a^2b^2)