simplify ln(50*7^x)

Solution

simplify

ln (50 \cdot 7^{x})

ln (50) + x ln (7)

Solution steps

ln (50 \cdot 7^{x})

Apply log rule:

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

ln (50 \cdot 7^{x}) = ln (50) + ln (7^{x})

= ln (50) + ln (7^{x})

Apply log rule:

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

ln (7^{x}) = x ln (7)

= ln (50) + x ln (7)

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

- lo g_{10} (3.72 \cdot 1 0^{- 5})

- lo g_{10} (7.21 \cdot 1 0^{- 7})

ln (- x) + ln (2)

- lo g_{10} (2.36 x 1 0^{- 3})