What is log_{10}(191.7x^{432}) ?

The solution to log_{10}(191.7x^{432}) is log_{10}(1917)+432log_{10}(x)-1

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simplify log_{10}(191.7x^{432})

simplify

lo g_{10} (191.7 x^{432})

lo g_{10} (1917) + 432 lo g_{10} (x) - 1

Solution steps

lo g_{10} (191.7 x^{432})

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{10} (191.7 x^{432}) = lo g_{10} (191.7) + lo g_{10} (x^{432})

= lo g_{10} (191.7) + lo g_{10} (x^{432})

lo g_{10} (191.7) = lo g_{10} (1917) - 1

lo g_{10} (x^{432}) = 432 lo g_{10} (x)

= lo g_{10} (1917) - 1 + 432 lo g_{10} (x)

Apply log rule:

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

432 lo g_{10} (x) = lo g_{10} (x^{432})

= lo g_{10} (1917) - 1 + lo g_{10} (x^{432})

Apply log rule:

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

lo g_{10} (1917) + lo g_{10} (x^{432}) = lo g_{10} (1917 x^{432})

= lo g_{10} (1917 x^{432}) - 1

Simplify

lo g_{10} (1917 x^{432}) : lo g_{10} (1917) + 432 lo g_{10} (x)

= lo g_{10} (1917) + 432 lo g_{10} (x) - 1

lo g_{10} (x (x - 1)^{2})

ln (x) - ln (x - 5000)

ln (8) + 4 ln (4)

ln (\frac{y}{y - 2})

ln (5) + ln (x) - ln (y)

What is log_{10}(191.7x^{432}) ?
The solution to log_{10}(191.7x^{432}) is log_{10}(1917)+432log_{10}(x)-1