Question

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Evaluate logarithmic expressions if possible. pls help

Answer 1

Explanation:

By the power property we know that 2*lnx = ln(x²)

Therefore 2*ln(x+6) = ln((x+6)²)

and 7*lnx = ln(x⁷)

finally by the product property we know that ln(a*b) = lna + lnb

so the recently transformed addition ln((x+6)²) + ln(x⁷) can be transformed into a product since the base of the logarithm are the same (base e for ln):

ln((x+6)²) + ln(x⁷) = ln(x⁷*(x+6)²)

if you would want to further develop it (a+b)²=a²+2*a*b+b²

=ln(x⁷*(x²+12x+36))

by the distributive property of multiplication you can bring x⁷ into the parentheses by multiplying each element inside:

=ln(x⁹+12x⁸+36x⁷)

And I believe that would be the condensation of the expression provided to a single logarithm with coefficient 1.

Answer 2

`ln(((x+6)^(2) )/(x^(7) ) )`

Explanation:

In photos.