What is log_{4}(8)+2log_{4}(7) ?

The solution to log_{4}(8)+2log_{4}(7) is log_{4}(392)

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simplify log_{4}(8)+2log_{4}(7)

simplify

lo g_{4} (8) + 2 lo g_{4} (7)

lo g_{4} (392)

Decimal Notation

4.30735 \dots

Solution steps

lo g_{4} (8) + 2 lo g_{4} (7)

Apply log rule:

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

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

= lo g_{4} (8) + lo g_{4} (7^{2})

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{4} (8) + lo g_{4} (7^{2}) = lo g_{4} (8 \cdot 7^{2})

= lo g_{4} (8 \cdot 7^{2})

8 \cdot 7^{2} = 392

= lo g_{4} (392)

ln (x x^{2} + y^{2})

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

\frac{1}{3} lo g_{2} (\frac{1}{3}) + \frac{2}{3} lo g_{2} (\frac{2}{3})

lo g_{10} (\frac{1 + x}{1 - x})

What is log_{4}(8)+2log_{4}(7) ?
The solution to log_{4}(8)+2log_{4}(7) is log_{4}(392)