What is 2ln(5)+3ln(4) ?

The solution to 2ln(5)+3ln(4) is 2ln(40)

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simplify 2ln(5)+3ln(4)

simplify

2 ln (5) + 3 ln (4)

2 ln (40)

Solution steps

2 ln (5) + 3 ln (4)

Apply log rule:

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

2 ln (5) = ln (5^{2})

= ln (5^{2}) + 3 ln (4)

Apply log rule:

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

3 ln (4) = ln (4^{3})

= ln (5^{2}) + ln (4^{3})

Apply log rule:

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

ln (5^{2}) + ln (4^{3}) = ln (4^{3} \cdot 5^{2})

= ln (4^{3} \cdot 5^{2})

5^{2} \cdot 4^{3} = 1600

= ln (1600)

Rewrite

1600

in power-base form:

1600 = 4 0^{2}

= ln (4 0^{2})

Apply log rule:

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

ln (4 0^{2}) = 2 ln (40)

= 2 ln (40)

ln (\frac{y}{c + x})

lo g_{2} (\frac{4 π ^{2}}{30})

ln (3 v + w) - ln (w) + 2 - ln (v)

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

7 lo g_{2} (y) - 4 lo g_{2} (x)