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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

∣ a ∣^{2}

(3 x^{3} \cdot y^{3})^{- 2}

(i + m)^{3}

e^{t} + e^{- 2} t

3 x + 2 x - 4 x

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