What is expand log_{4}(7^23^4) ?

The solution to expand log_{4}(7^23^4) is 2log_{4}(7)+4log_{4}(3)

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expand log_{4}(7^23^4)

expand

lo g_{4} (7^{2} 3^{4})

2 lo g_{4} (7) + 4 lo g_{4} (3)

Decimal Notation

5.97727 \dots

Solution steps

lo g_{4} (7^{2} \cdot 3^{4})

Apply log rule:

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

lo g_{4} (7^{2} \cdot 3^{4}) = lo g_{4} (7^{2}) + lo g_{4} (3^{4})

= lo g_{4} (7^{2}) + lo g_{4} (3^{4})

Apply log rule:

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

lo g_{4} (7^{2}) = 2 lo g_{4} (7)

= 2 lo g_{4} (7) + lo g_{4} (3^{4})

Apply log rule:

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

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

= 2 lo g_{4} (7) + 4 lo g_{4} (3)

ln (2 x y)

lo g_{2} (x + 1) - lo g_{2} (2 - x)

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

3 ln (x) - \frac{1}{3} ln (y)

\frac{1}{2} lo g_{10} (c) + 7 lo g_{10} (d)

What is expand log_{4}(7^23^4) ?
The solution to expand log_{4}(7^23^4) is 2log_{4}(7)+4log_{4}(3)