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

The solution to log_{4}(2)+2log_{4}(7) is log_{4}(98)

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

simplify

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

lo g_{4} (98)

Decimal Notation

3.30735 \dots

Solution steps

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

Apply log rule:

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

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

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

2 \cdot 7^{2} = 98

= lo g_{4} (98)

lo g_{2} (16 x)

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

lo g_{2} (\frac{8 x ^{2}}{y}) + lo g_{2} (2 x y)

lo g_{10} (\frac{z ^{5}}{x ^{3} y})

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

What is log_{4}(2)+2log_{4}(7) ?
The solution to log_{4}(2)+2log_{4}(7) is log_{4}(98)