What is expand log_{3}(9^2*2^4) ?

The solution to expand log_{3}(9^2*2^4) is 4+4log_{3}(2)

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expand log_{3}(9^2*2^4)

expand

lo g_{3} (9^{2} \cdot 2^{4})

4 + 4 lo g_{3} (2)

Decimal Notation

6.52371 \dots

Solution steps

lo g_{3} (9^{2} \cdot 2^{4})

Apply log rule:

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

lo g_{3} (9^{2} \cdot 2^{4}) = lo g_{3} (9^{2}) + lo g_{3} (2^{4})

= lo g_{3} (9^{2}) + lo g_{3} (2^{4})

Apply log rule:

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

lo g_{3} (9^{2}) = 2 lo g_{3} (9)

= 2 lo g_{3} (9) + lo g_{3} (2^{4})

Apply log rule:

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

lo g_{3} (2^{4}) = 4 lo g_{3} (2)

= 2 lo g_{3} (9) + 4 lo g_{3} (2)

2 lo g_{3} (9) = 4

= 4 + 4 lo g_{3} (2)

ln (x^{7} 2 - x)

lo g_{b} (7) + 2 lo g_{b} (2)

lo g_{a} (4 x^{5} y)

lo g_{10} (100 y)

ln (\frac{x ^{2} - 1}{x ^{9}})

What is expand log_{3}(9^2*2^4) ?
The solution to expand log_{3}(9^2*2^4) is 4+4log_{3}(2)