Question

Rewrite the expression ln sqroot((x+1)/(x+2)) in an equivalent way that involves no roots, powers, products, or quotients.

Answer 1

\[\ln \sqrt{(x+1)/(x+2)}\]

Answer 2

use logarithmic expansion

Answer 3

Log Rules:

1) log_b(mn) = log_b(m) + log_b(n)

2) log_b(m/n) = log_b(m) – log_b(n)

3) log_b(m^n) = n · log_b(m)

Answer 4

\[=\ln \left[ (x+1) /(x+2)\right]^{1/2}=1/2*\ln (x+1)/(x+2)=\frac{ 1 }{ 2 } \ln (x+1)-\frac{ 1 }{ 2 }\ln(x+2)\]

Answer 5

that was easy wasn't it?

Answer 6

1) Multiplication inside the log can be turned into addition outside the log, and vice versa.

2) Division inside the log can be turned into subtraction outside the log, and vice versa.

3) An exponent on everything inside a log can be moved out front as a multiplier, and vice versa.

Warning: Just as when you're dealing with exponents, the above rules work only if the bases are the same.

Source: http://www.purplemath.com/modules/logrules.htm