What is 2log_{10}(x)-6log_{10}(x-9) ?

The solution to 2log_{10}(x)-6log_{10}(x-9) is log_{10}((x^2)/((x-9)^6))

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simplify 2log_{10}(x)-6log_{10}(x-9)

simplify

2 lo g_{10} (x) - 6 lo g_{10} (x - 9)

lo g_{10} (\frac{x ^{2}}{( x - 9 ) ^{6}})

Solution steps

2 lo g_{10} (x) - 6 lo g_{10} (x - 9)

Apply log rule:

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

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

= lo g_{10} (x^{2}) - 6 lo g_{10} (x - 9)

Apply log rule:

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

6 lo g_{10} (x - 9) = lo g_{10} ((x - 9)^{6})

= lo g_{10} (x^{2}) - lo g_{10} ((x - 9)^{6})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{10} (x^{2}) - lo g_{10} ((x - 9)^{6}) = lo g_{10} (\frac{x ^{2}}{( x - 9 ) ^{6}})

= lo g_{10} (\frac{x ^{2}}{( x - 9 ) ^{6}})

ln (x) - ln (6)

\frac{95}{100} \cdot ln (5 \cdot 1 0^{6}) + \frac{5}{100} \cdot ln (1000)

ln (\frac{x}{y}) - ln (\frac{a}{b})

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

- \frac{1}{2} ln (5 - 2 x) - ln (x)

What is 2log_{10}(x)-6log_{10}(x-9) ?
The solution to 2log_{10}(x)-6log_{10}(x-9) is log_{10}((x^2)/((x-9)^6))