What is expand log_{7}((3^6)/(5*8^4)) ?

The solution to expand log_{7}((3^6)/(5*8^4)) is 6log_{7}(3)-log_{7}(5)-12log_{7}(2)

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expand log_{7}((3^6)/(5*8^4))

expand

lo g_{7} (\frac{3 ^{6}}{5 \cdot 8 ^{4}})

6 lo g_{7} (3) - lo g_{7} (5) - 12 lo g_{7} (2)

Decimal Notation

- 1.71412 \dots

Solution steps

lo g_{7} (\frac{3 ^{6}}{5 \cdot 8 ^{4}})

Apply log rule:

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

lo g_{7} (\frac{3 ^{6}}{5 \cdot 8 ^{4}}) = lo g_{7} (3^{6}) - lo g_{7} (5 \cdot 8^{4})

= lo g_{7} (3^{6}) - lo g_{7} (8^{4} \cdot 5)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{7} (3^{6}) = 6 lo g_{7} (3)

= 6 lo g_{7} (3) - lo g_{7} (5 \cdot 8^{4})

Apply log rule:

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

lo g_{7} (5 \cdot 8^{4}) = lo g_{7} (5) + lo g_{7} (8^{4})

= 6 lo g_{7} (3) - (lo g_{7} (5) + lo g_{7} (8^{4}))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{7} (8^{4}) = 4 lo g_{7} (8)

= 6 lo g_{7} (3) - (lo g_{7} (5) + 4 lo g_{7} (8))

4 lo g_{7} (8) = 12 lo g_{7} (2)

= 6 lo g_{7} (3) - (12 lo g_{7} (2) + lo g_{7} (5))

- (lo g_{7} (5) + 12 lo g_{7} (2)) : - lo g_{7} (5) - 12 lo g_{7} (2)

= 6 lo g_{7} (3) - lo g_{7} (5) - 12 lo g_{7} (2)

ln (\frac{- v ^{2}}{2 α e ^{- β s}})

\frac{2}{3} ln (3 - x) - \frac{1}{3} ln (3 + x)

- lo g_{10} (6 \cdot 1 0^{- 7})

ln (\frac{6.5}{2.5})

ln (\frac{π}{4}) \cdot \frac{π}{4}

What is expand log_{7}((3^6)/(5*8^4)) ?
The solution to expand log_{7}((3^6)/(5*8^4)) is 6log_{7}(3)-log_{7}(5)-12log_{7}(2)