What is expand log_{9}(((3^3)/7)^4) ?

The solution to expand log_{9}(((3^3)/7)^4) is 4(3/2-log_{9}(7))

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expand log_{9}(((3^3)/7)^4)

expand

lo g_{9} ((\frac{3 ^{3}}{7})^{4})

4 (\frac{3}{2} - lo g_{9} (7))

Decimal Notation

2.45751 \dots

Solution steps

lo g_{9} ((\frac{3 ^{3}}{7})^{4})

Apply log rule:

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

lo g_{9} ((\frac{3 ^{3}}{7})^{4}) = 4 lo g_{9} (\frac{3 ^{3}}{7})

= 4 lo g_{9} (\frac{3 ^{3}}{7})

Apply log rule:

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

lo g_{9} (\frac{3 ^{3}}{7}) = lo g_{9} (3^{3}) - lo g_{9} (7)

= 4 (lo g_{9} (3^{3}) - lo g_{9} (7))

Apply log rule:

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

lo g_{9} (3^{3}) = 3 lo g_{9} (3)

= 4 (3 lo g_{9} (3) - lo g_{9} (7))

3 lo g_{9} (3) = \frac{3}{2}

= 4 (\frac{3}{2} - lo g_{9} (7))

2 ln ∣ ln (x) ∣ + ln (x)

\frac{\frac{3}{l n ( 7 ) - l n ( 4 )}}{3 x + 4}

- lo g_{10} (7.1 \cdot 1 0^{- 7})

5 ln (2) + 3 ln (x) - \frac{1}{2} ln (x + 9)

- \frac{ln ( 0.965 ) - ln ( \frac{190}{749} )}{0.01 ln ( 0.965 )}

What is expand log_{9}(((3^3)/7)^4) ?
The solution to expand log_{9}(((3^3)/7)^4) is 4(3/2-log_{9}(7))