What is 5log_{10}(3)+log_{10}(4) ?

The solution to 5log_{10}(3)+log_{10}(4) is log_{10}(972)

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simplify 5log_{10}(3)+log_{10}(4)

simplify

5 lo g_{10} (3) + lo g_{10} (4)

lo g_{10} (972)

Decimal Notation

2.98766 \dots

Solution steps

5 lo g_{10} (3) + lo g_{10} (4)

Apply log rule:

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

5 lo g_{10} (3) = lo g_{10} (3^{5})

= lo g_{10} (3^{5}) + lo g_{10} (4)

Apply log rule:

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

lo g_{10} (3^{5}) + lo g_{10} (4) = lo g_{10} (3^{5} \cdot 4)

= lo g_{10} (3^{5} \cdot 4)

3^{5} \cdot 4 = 972

= lo g_{10} (972)

lo g_{10} (k^{2} - 100) - lo g_{10} (k) - 10

ln (\frac{3 d}{4 ^{- 1}})

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

lo g_{10} (5 \cdot 3)

ln (\frac{1}{25 k})

What is 5log_{10}(3)+log_{10}(4) ?
The solution to 5log_{10}(3)+log_{10}(4) is log_{10}(972)