What is ln(3^{x-2}(3^x-10)) ?

The solution to ln(3^{x-2}(3^x-10)) is (x-2)ln(3)+ln(3^x-10)

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simplify ln(3^{x-2}(3^x-10))

simplify

ln (3^{x - 2} (3^{x} - 10))

(x - 2) ln (3) + ln (3^{x} - 10)

Solution steps

ln (3^{x - 2} (3^{x} - 10))

Apply log rule:

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

ln (3^{x - 2} (3^{x} - 10)) = ln (3^{x - 2}) + ln (3^{x} - 10)

= ln (3^{x - 2}) + ln (3^{x} - 10)

Apply log rule:

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

ln (3^{x - 2}) = (x - 2) ln (3)

= (x - 2) ln (3) + ln (3^{x} - 10)

ln (ux)

ln (x^{3} y^{3})

3 ln (x^{2}) - ln (x)

2 lo g_{6} (u) + 6 lo g_{6} (v)

- 4 ln (x - 2) + 3 ln (1 - x)

What is ln(3^{x-2}(3^x-10)) ?
The solution to ln(3^{x-2}(3^x-10)) is (x-2)ln(3)+ln(3^x-10)