simplify ln(7*10^1)

Solution

simplify

ln (7 \cdot 1 0^{1})

ln (7) + ln (10)

Decimal Notation

4.24849 \dots

Solution steps

ln (7 \cdot 1 0^{1})

Apply log rule:

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

ln (7 \cdot 1 0^{1}) = ln (7) + ln (1 0^{1})

= ln (7) + ln (1 0^{1})

Apply log rule:

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

ln (1 0^{1}) = 1 \cdot ln (10)

= ln (7) + 1 \cdot ln (10)

Multiply:

1 \cdot ln (10) = ln (10)

= ln (7) + ln (10)

ln (3 \cdot 3.71 2^{2})

(6 e) ln (2 e) - 3

ln (77) - ln (5)

ln (x) - 5 [ln (x - 8) + ln (x + 8)]

\frac{9}{2} \cdot ln (2)