What is log_{3}(a^7)+(log_{3}(a^4)-2log_{3}(b)) ?

The solution to log_{3}(a^7)+(log_{3}(a^4)-2log_{3}(b)) is log_{3}((a^{11})/(b^2))

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simplify log_{3}(a^7)+(log_{3}(a^4)-2log_{3}(b))

simplify

lo g_{3} (a^{7}) + (lo g_{3} (a^{4}) - 2 lo g_{3} (b))

lo g_{3} (\frac{a ^{11}}{b ^{2}})

Solution steps

lo g_{3} (a^{7}) + (lo g_{3} (a^{4}) - 2 lo g_{3} (b))

Apply log rule:

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

2 lo g_{3} (b) = lo g_{3} (b^{2})

= lo g_{3} (a^{7}) + (lo g_{3} (a^{4}) - lo g_{3} (b^{2}))

Apply log rule:

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

lo g_{3} (a^{4}) - lo g_{3} (b^{2}) = lo g_{3} (\frac{a ^{4}}{b ^{2}})

= lo g_{3} (a^{7}) + + lo g_{3} (\frac{a ^{4}}{b ^{2}})

Apply log rule:

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

lo g_{3} (a^{7}) + lo g_{3} (\frac{a ^{4}}{b ^{2}}) = lo g_{3} (\frac{a ^{4}}{b ^{2}} a^{7})

= lo g_{3} (\frac{a ^{4}}{b ^{2}} a^{7})

Simplify

a^{7} \frac{a ^{4}}{b ^{2}} : \frac{a ^{11}}{b ^{2}}

= lo g_{3} (\frac{a ^{11}}{b ^{2}})

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

ln (\frac{e ^{9}}{17})

- lo g_{10} (7.9 \cdot 1 0^{- 4})

- lo g_{10} (1 x 1 0^{- 2})

\frac{2 ln ( \frac{55}{9} )}{ln ( 2 )} - 16

What is log_{3}(a^7)+(log_{3}(a^4)-2log_{3}(b)) ?
The solution to log_{3}(a^7)+(log_{3}(a^4)-2log_{3}(b)) is log_{3}((a^{11})/(b^2))