simplify ln(2*5^2)

Solution

simplify

ln (2 \cdot 5^{2})

ln (2) + 2 ln (5)

Decimal Notation

3.91202 \dots

Solution steps

ln (2 \cdot 5^{2})

Apply log rule:

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

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

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

Apply log rule:

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

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

= ln (2) + 2 ln (5)

ln (2 e) - 1

lo g_{7} (4)

\frac{1}{2} (ln (y - 1) - ln (y + 1))

ln (3^{2}) + ln (2^{7})

ln (\frac{200}{215})