What is 2log_{10}(x)+7log_{10}(x-9) ?

The solution to 2log_{10}(x)+7log_{10}(x-9) is log_{10}(x^2(x-9)^7)

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simplify 2log_{10}(x)+7log_{10}(x-9)

simplify

2 lo g_{10} (x) + 7 lo g_{10} (x - 9)

lo g_{10} (x^{2} (x - 9)^{7})

Solution steps

2 lo g_{10} (x) + 7 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}) + 7 lo g_{10} (x - 9)

Apply log rule:

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

7 lo g_{10} (x - 9) = lo g_{10} ((x - 9)^{7})

= lo g_{10} (x^{2}) + lo g_{10} ((x - 9)^{7})

Apply log rule:

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

lo g_{10} (x^{2}) + lo g_{10} ((x - 9)^{7}) = lo g_{10} (x^{2} (x - 9)^{7})

= lo g_{10} (x^{2} (x - 9)^{7})

1.005 \cdot ln (1.687) - 0.287 \cdot ln (4.5)

ln^{2} (x) + 2 ln (x)

ln (\frac{0.75}{0.691 \cdot 1 0 ^{11}})

ln ((\frac{2}{x})^{5} \cdot 20)

ln (1 + x) - ln (x)

What is 2log_{10}(x)+7log_{10}(x-9) ?
The solution to 2log_{10}(x)+7log_{10}(x-9) is log_{10}(x^2(x-9)^7)