What is 9log_{10}(7)-5log_{10}(23) ?

The solution to 9log_{10}(7)-5log_{10}(23) is log_{10}(40353607/6436343)

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simplify 9log_{10}(7)-5log_{10}(23)

simplify

9 lo g_{10} (7) - 5 lo g_{10} (23)

lo g_{10} (\frac{40353607}{6436343})

Decimal Notation

0.79724 \dots

Solution steps

9 lo g_{10} (7) - 5 lo g_{10} (23)

Apply log rule:

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

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

= lo g_{10} (7^{9}) - 5 lo g_{10} (23)

Apply log rule:

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

5 lo g_{10} (23) = lo g_{10} (2 3^{5})

= lo g_{10} (7^{9}) - lo g_{10} (2 3^{5})

Apply log rule:

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

lo g_{10} (7^{9}) - lo g_{10} (2 3^{5}) = lo g_{10} (\frac{7 ^{9}}{2 3 ^{5}})

= lo g_{10} (\frac{7 ^{9}}{2 3 ^{5}})

\frac{7 ^{9}}{2 3 ^{5}} = \frac{40353607}{6436343}

= lo g_{10} (\frac{40353607}{6436343})

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

ln (\frac{x ^{5}}{y ^{6}})

ln ((x - 1)^{x}) + ln (e^{- x})

- lo g_{10} (3.6 \cdot 1 0^{- 7})

ln (x^{2} 1 0^{2 x})

What is 9log_{10}(7)-5log_{10}(23) ?
The solution to 9log_{10}(7)-5log_{10}(23) is log_{10}(40353607/6436343)