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

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

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

simplify

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

lo g_{10} (2)

Decimal Notation

0.30102 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{10} (2^{3} x) - lo g_{10} (4 x) = lo g_{10} (\frac{2 ^{3} x}{4 x})

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

Cancel

\frac{2 ^{3} x}{4 x} : 2

= lo g_{10} (2)

lo g_{10} (5 x + 7) - lo g_{10} (x)

ln (9) - ln (2)

lo g_{10} (\frac{n}{2})

ln ∣ 7 - 2 ∣ - \frac{3}{2} ln ∣ 2 (7) - 1 ∣ + 2 ln ∣ 7 + 3 ∣

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

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