What is 360log_{10}(3)-720log_{10}(5) ?

The solution to 360log_{10}(3)-720log_{10}(5) is log_{10}((3^{360})/5)*720

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simplify 360log_{10}(3)-720log_{10}(5)

simplify

360 lo g_{10} (3) - 720 lo g_{10} (5)

lo g_{10} (\frac{3 ^{360}}{5}) \cdot 720

Decimal Notation

123166.57082 \dots

Solution steps

360 lo g_{10} (3) - 720 lo g_{10} (5)

Apply log rule:

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

360 lo g_{10} (3) = lo g_{10} (3^{360})

= lo g_{10} (3^{360}) - 720 lo g_{10} (5)

Apply log rule:

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

lo g_{10} (3^{360}) - lo g_{10} (5) = lo g_{10} (\frac{3 ^{360}}{5})

= lo g_{10} (\frac{3 ^{360}}{5}) \cdot 720

\frac{2 ln ( 3 ) - ln ( 2 )}{2 ln ( 3 ) - 3 ln ( 2 )}

0.026 ln (\frac{0.702}{8 \cdot 1 0 ^{- 16}})

lo g_{3} (\frac{6 x ^{5}}{7 w ^{2} y ^{3}})

4 (lo g_{a} (x) - 5 lo g_{a} (y)) + 3 lo g_{a} (z)

- 3 ln ∣ x + 2 ∣ + x - ln ∣ x - 2 ∣

What is 360log_{10}(3)-720log_{10}(5) ?
The solution to 360log_{10}(3)-720log_{10}(5) is log_{10}((3^{360})/5)*720