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Popular >

simplify ln(((4m^5))/p)

Solution

simplify

ln (\frac{( 4 m ^{5} )}{p})

Solution

2 ln (2) + 5 ln (m) - ln (p)

Solution steps

ln (\frac{( 4 m ^{5} )}{p})

Apply log rule:

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

ln (\frac{( 4 m ^{5} )}{p}) = ln ((4 m^{5})) - ln (p)

= ln (4 m^{5}) - ln (p)

Apply log rule:

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

ln (4 m^{5}) = ln (4) + ln (m^{5})

= ln (4) + ln (m^{5}) - ln (p)

Apply log rule:

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

ln (m^{5}) = 5 ln (m)

= ln (4) + 5 ln (m) - ln (p)

ln (4) = 2 ln (2)

= 2 ln (2) + 5 ln (m) - ln (p)

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Frequently Asked Questions (FAQ)

What is ln(((4m^5))/p) ?
The solution to ln(((4m^5))/p) is 2ln(2)+5ln(m)-ln(p)