What is ln(5x^2)+ln(2x)-ln(x^3) ?

The solution to ln(5x^2)+ln(2x)-ln(x^3) is ln(10)

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simplify ln(5x^2)+ln(2x)-ln(x^3)

simplify

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

ln (10)

Decimal Notation

2.30258 \dots

Solution steps

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

Apply log rule:

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

ln (5 x^{2}) + ln (2 x) = ln (5 \cdot 2 x^{2} x)

= ln (5 \cdot 2 x^{2} x) - ln (x^{3})

Simplify

5 x^{2} \cdot 2 x : 10 x^{3}

= ln (10 x^{3}) - ln (x^{3})

Apply log rule:

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

ln (10 x^{3}) - ln (x^{3}) = ln (\frac{10 x ^{3}}{x ^{3}})

= ln (\frac{10 x ^{3}}{x ^{3}})

Cancel the common factor:

x^{3}

= ln (10)

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What is ln(5x^2)+ln(2x)-ln(x^3) ?
The solution to ln(5x^2)+ln(2x)-ln(x^3) is ln(10)