What is ln(8x)-2ln(2x)+3ln(2x^2) ?

The solution to ln(8x)-2ln(2x)+3ln(2x^2) is ln(16x^5)

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simplify ln(8x)-2ln(2x)+3ln(2x^2)

simplify

ln (8 x) - 2 ln (2 x) + 3 ln (2 x^{2})

ln (16 x^{5})

Solution steps

ln (8 x) - 2 ln (2 x) + 3 ln (2 x^{2})

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (2 x) = ln ((2 x)^{2})

= ln (8 x) - ln ((2 x)^{2}) + 3 ln (2 x^{2})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (8 x) - ln ((2 x)^{2}) = ln (\frac{8 x}{( 2 x ) ^{2}})

= ln (\frac{8 x}{( 2 x ) ^{2}}) + 3 ln (2 x^{2})

Simplify

\frac{8 x}{( 2 x ) ^{2}} : \frac{2}{x}

= ln (\frac{2}{x}) + 3 ln (2 x^{2})

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 ln (2 x^{2}) = ln ((2 x^{2})^{3})

= ln (\frac{2}{x}) + ln ((2 x^{2})^{3})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (\frac{2}{x}) + ln ((2 x^{2})^{3}) = ln (\frac{2}{x} (2 x^{2})^{3})

= ln (\frac{2}{x} (2 x^{2})^{3})

Simplify

\frac{2}{x} (2 x^{2})^{3} : 16 x^{5}

= ln (16 x^{5})

\frac{2}{7} \cdot ln ∣ 65 - 6 ∣ + \frac{5}{7} \cdot ln ∣ 65 + 1 ∣

5 \cdot lo g_{10} (x) - 3 \cdot lo g_{10} (y)

ln (\frac{2 d x}{x})

ln ((x) (x - 3))

- lo g_{10} (8 \cdot 1 0^{- 4})

What is ln(8x)-2ln(2x)+3ln(2x^2) ?
The solution to ln(8x)-2ln(2x)+3ln(2x^2) is ln(16x^5)