What is expand log_{6}(((12/7)^5)^5) ?

The solution to expand log_{6}(((12/7)^5)^5) is 25log_{6}(12/7)

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expand log_{6}(((12/7)^5)^5)

expand

lo g_{6} ((\frac{12}{7})^{5})^{5}

25 lo g_{6} (\frac{12}{7})

Decimal Notation

7.52049 \dots

Solution steps

lo g_{6} ((\frac{12}{7})^{5})^{5}

Apply log rule:

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

lo g_{6} ((\frac{12}{7})^{5})^{5} = 5 lo g_{6} ((\frac{12}{7})^{5})

= 5 lo g_{6} ((\frac{12}{7})^{5})

Apply log rule:

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

lo g_{6} ((\frac{12}{7})^{5}) = 5 lo g_{6} (\frac{12}{7})

= 5 \cdot 5 lo g_{6} (\frac{12}{7})

Multiply the numbers:

5 \cdot 5 = 25

= 25 lo g_{6} (\frac{12}{7})

lo g_{10} (\frac{x ^{6} y ^{18}}{z ^{14}})

- 50 ln (\frac{13}{16})

- ln (\frac{10}{60})

ln (\frac{( 2 ^{- 4} )}{( 3 ^{3} 5 ^{3} )})

\frac{ln ( \frac{11664}{29} )}{2 ln ( 6 )}

What is expand log_{6}(((12/7)^5)^5) ?
The solution to expand log_{6}(((12/7)^5)^5) is 25log_{6}(12/7)