What is 2log_{10}(2)+4log_{10}(3) ?

The solution to 2log_{10}(2)+4log_{10}(3) is 2log_{10}(18)

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simplify 2log_{10}(2)+4log_{10}(3)

simplify

2 lo g_{10} (2) + 4 lo g_{10} (3)

2 lo g_{10} (18)

Decimal Notation

2.51054 \dots

Solution steps

2 lo g_{10} (2) + 4 lo g_{10} (3)

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

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

= lo g_{10} (2^{2}) + lo g_{10} (3^{4})

Apply log rule:

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

lo g_{10} (2^{2}) + lo g_{10} (3^{4}) = lo g_{10} (2^{2} \cdot 3^{4})

= lo g_{10} (2^{2} \cdot 3^{4})

2^{2} \cdot 3^{4} = 324

= lo g_{10} (324)

Factor the number:

324 = 1 8^{2}

= lo g_{10} (1 8^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

lo g_{10} (1 8^{2}) = 2 lo g_{10} (18)

= 2 lo g_{10} (18)

lo g_{10} (k) - 5 lo g_{10} (g)

lo g_{4} (5 x)

\frac{1}{2} ln (x) - \frac{2}{3} ln (y) - \frac{1}{4} ln (z)

ln (x - 3) + 2 ln (x)

ln (x - 1) - ln (x)

What is 2log_{10}(2)+4log_{10}(3) ?
The solution to 2log_{10}(2)+4log_{10}(3) is 2log_{10}(18)