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Popular >

simplify ln((x^2g)/(xv))

Solution

simplify

ln (\frac{x ^{2} \cdot g}{x \cdot v})

Solution

ln (x) + ln (g) - ln (v)

Solution steps

ln (\frac{x ^{2} g}{xv})

Apply log rule:

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

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

= ln (x^{2} g) - ln (xv)

Apply log rule:

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

ln (x^{2} g) = ln (x^{2}) + ln (g), ln (xv) = ln (x) + ln (v)

= ln (x^{2}) + ln (g) - (ln (x) + ln (v))

Apply log rule:

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

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

= 2 ln (x) + ln (g) - (ln (x) + ln (v))

- (ln (x) + ln (v)) : - ln (x) - ln (v)

= 2 ln (x) + ln (g) - ln (x) - ln (v)

Simplify

2 ln (x) + ln (g) - ln (x) - ln (v) : ln (x) + ln (g) - ln (v)

= ln (x) + ln (g) - ln (v)

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Frequently Asked Questions (FAQ)

What is ln((x^2*g)/(x*v)) ?
The solution to ln((x^2*g)/(x*v)) is ln(x)+ln(g)-ln(v)