What is expand log_{9}((8^2)/(5^4)) ?

The solution to expand log_{9}((8^2)/(5^4)) is 6log_{9}(2)-4log_{9}(5)

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expand log_{9}((8^2)/(5^4))

expand

lo g_{9} (\frac{8 ^{2}}{5 ^{4}})

6 lo g_{9} (2) - 4 lo g_{9} (5)

Decimal Notation

- 1.03715 \dots

Solution steps

lo g_{9} (\frac{8 ^{2}}{5 ^{4}})

Apply log rule:

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

lo g_{9} (\frac{8 ^{2}}{5 ^{4}}) = lo g_{9} (8^{2}) - lo g_{9} (5^{4})

= lo g_{9} (8^{2}) - lo g_{9} (5^{4})

Apply log rule:

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

lo g_{9} (8^{2}) = 2 lo g_{9} (8)

= 2 lo g_{9} (8) - lo g_{9} (5^{4})

Apply log rule:

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

lo g_{9} (5^{4}) = 4 lo g_{9} (5)

= 2 lo g_{9} (8) - 4 lo g_{9} (5)

2 lo g_{9} (8) = 6 lo g_{9} (2)

= 6 lo g_{9} (2) - 4 lo g_{9} (5)

4 lo g_{3} (x) + 2 lo g_{3} (y)

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

2.69 - \frac{0.02569}{2} ln (\frac{0. 4 ^{3}}{2 ^{2}})

\frac{1}{3} ln (5)

- (- \frac{1}{3} ln (5 + 1) + \frac{1}{3} ln (5 - 2))

What is expand log_{9}((8^2)/(5^4)) ?
The solution to expand log_{9}((8^2)/(5^4)) is 6log_{9}(2)-4log_{9}(5)