What is log_{10}((a^3b^2)/(c^4)) ?

The solution to log_{10}((a^3b^2)/(c^4)) is 3log_{10}(a)+2log_{10}(b)-4log_{10}(c)

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simplify log_{10}((a^3b^2)/(c^4))

simplify

lo g_{10} (\frac{a ^{3} b ^{2}}{c ^{4}})

3 lo g_{10} (a) + 2 lo g_{10} (b) - 4 lo g_{10} (c)

Solution steps

lo g_{10} (\frac{a ^{3} b ^{2}}{c ^{4}})

Apply log rule:

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

lo g_{10} (\frac{a ^{3} b ^{2}}{c ^{4}}) = lo g_{10} (a^{3} b^{2}) - lo g_{10} (c^{4})

= lo g_{10} (a^{3} b^{2}) - lo g_{10} (c^{4})

lo g_{10} (a^{3} b^{2}) = 3 lo g_{10} (a) + 2 lo g_{10} (b)

lo g_{10} (c^{4}) = 4 lo g_{10} (c)

= 3 lo g_{10} (a) + 2 lo g_{10} (b) - 4 lo g_{10} (c)

lo g_{\frac{1}{2}} (\frac{3}{4})

4 lo g_{10} (3) + lo g_{10} (2)

lo g_{10} (x^{3}) - lo g_{10} (y^{2})

\frac{1}{3} ln (x - 3) - 4 ln (z) + ln (y + 7)

lo g_{10} ((\frac{p ^{4}}{q ^{7}})^{2})

What is log_{10}((a^3b^2)/(c^4)) ?
The solution to log_{10}((a^3b^2)/(c^4)) is 3log_{10}(a)+2log_{10}(b)-4log_{10}(c)