What is 4log_{10}(a)-5log_{10}(b) ?

The solution to 4log_{10}(a)-5log_{10}(b) is log_{10}((a^4)/(b^5))

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simplify 4log_{10}(a)-5log_{10}(b)

simplify

4 lo g_{10} (a) - 5 lo g_{10} (b)

lo g_{10} (\frac{a ^{4}}{b ^{5}})

Solution steps

4 lo g_{10} (a) - 5 lo g_{10} (b)

Apply log rule:

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

4 lo g_{10} (a) = lo g_{10} (a^{4})

= lo g_{10} (a^{4}) - 5 lo g_{10} (b)

Apply log rule:

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

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

= lo g_{10} (a^{4}) - lo g_{10} (b^{5})

Apply log rule:

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

lo g_{10} (a^{4}) - lo g_{10} (b^{5}) = lo g_{10} (\frac{a ^{4}}{b ^{5}})

= lo g_{10} (\frac{a ^{4}}{b ^{5}})

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

- 2 ln (cos (\frac{y ^{4}}{4}) + C)

ln (∣ x ∣^{\frac{1}{2}} ∣ x - 6 ∣^{\frac{1}{2}})

- 1 \cdot ln (\frac{x}{y})

ln (\frac{565000}{350000})

What is 4log_{10}(a)-5log_{10}(b) ?
The solution to 4log_{10}(a)-5log_{10}(b) is log_{10}((a^4)/(b^5))