What is log_{10}(x^6)-log_{10}(x^5) ?

The solution to log_{10}(x^6)-log_{10}(x^5) is log_{10}(x)

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simplify log_{10}(x^6)-log_{10}(x^5)

simplify

lo g_{10} (x^{6}) - lo g_{10} (x^{5})

lo g_{10} (x)

Solution steps

lo g_{10} (x^{6}) - lo g_{10} (x^{5})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), assuming x > 0

lo g_{10} (x^{6}) = 6 lo g_{10} (x)

= 6 lo g_{10} (x) - lo g_{10} (x^{5})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), assuming x > 0

lo g_{10} (x^{5}) = 5 lo g_{10} (x)

= 6 lo g_{10} (x) - 5 lo g_{10} (x)

Add similar elements:

6 lo g_{10} (x) - 5 lo g_{10} (x) = lo g_{10} (x)

= lo g_{10} (x)

lo g_{10} (24) - lo g_{10} (3) + lo g_{10} (16)

lo g_{2} (9) - lo g_{2} (11)

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

\frac{1}{2} lo g_{2} (5) - 2 lo g_{2} (6)

6 [6 ln (x) - ln (x + 6) - ln (x - 6)]

What is log_{10}(x^6)-log_{10}(x^5) ?
The solution to log_{10}(x^6)-log_{10}(x^5) is log_{10}(x)