What is 5log_{10}(2)+log_{10}(3) ?

The solution to 5log_{10}(2)+log_{10}(3) is log_{10}(96)

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simplify 5log_{10}(2)+log_{10}(3)

simplify

5 lo g_{10} (2) + lo g_{10} (3)

lo g_{10} (96)

Decimal Notation

1.98227 \dots

Solution steps

5 lo g_{10} (2) + lo g_{10} (3)

Apply log rule:

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

5 lo g_{10} (2) = lo g_{10} (2^{5})

= lo g_{10} (2^{5}) + lo g_{10} (3)

Apply log rule:

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

lo g_{10} (2^{5}) + lo g_{10} (3) = lo g_{10} (2^{5} \cdot 3)

= lo g_{10} (2^{5} \cdot 3)

2^{5} \cdot 3 = 96

= lo g_{10} (96)

- 0.9 lo g_{2} (0.9) - 0.1 lo g_{2} (0.1)

lo g_{m} (\frac{a \cdot b \cdot c ^{\frac{1}{4}}}{d \cdot e ^{\frac{1}{2}}})

ln (4 x^{3})

ln (2 x (x + 3)^{5})

What is 5log_{10}(2)+log_{10}(3) ?
The solution to 5log_{10}(2)+log_{10}(3) is log_{10}(96)