What is simplify-ln(25/16) ?

The solution to simplify-ln(25/16) is -2ln(5)+4ln(2)

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simplify-ln(25/16)

simplify

- ln (\frac{25}{16})

- 2 ln (5) + 4 ln (2)

Decimal Notation

- 0.44628 \dots

Solution steps

- ln (\frac{25}{16})

Apply log rule:

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

ln (\frac{25}{16}) = ln (25) - ln (16)

= - (ln (25) - ln (16))

ln (25) = 2 ln (5)

ln (16) = 4 ln (2)

= - (2 ln (5) - 4 ln (2))

Distribute parentheses

= - (2 ln (5)) - (- 4 ln (2))

Apply minus-plus rules

- (- a) = a, - (a) = - a

= - 2 ln (5) + 4 ln (2)

lo g_{9} (u \cdot v \cdot w)

ln (3) \frac{1}{2}

- \frac{6 ln ( 60 )}{ln ( 2 )}

lo g_{5} (28) x^{2} - lo g_{5} (2 x)

20 \cdot lo g_{\frac{6}{5}} (20)

What is simplify-ln(25/16) ?
The solution to simplify-ln(25/16) is -2ln(5)+4ln(2)