What is log_{10}((x^8y^8)/(z^{20)}) ?

The solution to log_{10}((x^8y^8)/(z^{20)}) is 8log_{10}(x)+8log_{10}(y)-20log_{10}(z)

Popular >

simplify log_{10}((x^8y^8)/(z^{20)})

simplify

lo g_{10} (\frac{x ^{8} y ^{8}}{z ^{20}})

8 lo g_{10} (x) + 8 lo g_{10} (y) - 20 lo g_{10} (z)

Solution steps

lo g_{10} (\frac{x ^{8} y ^{8}}{z ^{20}})

Apply log rule:

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

lo g_{10} (\frac{x ^{8} y ^{8}}{z ^{20}}) = lo g_{10} (x^{8} y^{8}) - lo g_{10} (z^{20})

= lo g_{10} (x^{8} y^{8}) - lo g_{10} (z^{20})

lo g_{10} (x^{8} y^{8}) = 8 lo g_{10} (x) + 8 lo g_{10} (y)

lo g_{10} (z^{20}) = 20 lo g_{10} (z)

= 8 lo g_{10} (x) + 8 lo g_{10} (y) - 20 lo g_{10} (z)

lo g_{10} (x^{2} + 3 x - 40) - lo g_{10} (x^{2} - 64)

3 lo g_{a} (2 x + 1) - 2 lo g_{a} (2 x - 1)

5 lo g_{10} (x) + 6 lo g_{10} (y)

ln (6) - ln (3) + ln (2 x)

What is log_{10}((x^8y^8)/(z^{20)}) ?
The solution to log_{10}((x^8y^8)/(z^{20)}) is 8log_{10}(x)+8log_{10}(y)-20log_{10}(z)