simplify ln(x500^x)

Solution

simplify

ln (x 50 0^{x})

ln (x) + x ln (500)

Solution steps

ln (x \cdot 50 0^{x})

Apply log rule:

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

ln (x \cdot 50 0^{x}) = ln (x) + ln (50 0^{x})

= ln (x) + ln (50 0^{x})

Apply log rule:

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

ln (50 0^{x}) = x ln (500)

= ln (x) + x ln (500)

lo g_{10} (3 x) + lo g_{10} (x + 2) 7

- lo g_{10} (9 \cdot 1 0^{- 10})

ln (1 - 2 y) - ln (1 - y)

lo g_{3} (\frac{1}{9 ∣ 49})

lo g_{10} (0.5) - lo g_{10} (x)