logarithm expansion

Question

I am doing very well with logs, but I cannot figure out this problem.  Can anyone help me???

Expand log7(2x-3)^2

(The log 7 IS NOT log base 7, it is log base 10 of 7).

Answer 1

log(7(2x-3)^2)

 

Use the product rule first.

 

log(AB) = log(A) + log(b)

 

log(7) + log(2x-3)^2

 

Next use the power rule

 

log(A^r) = rlog(A)

 

log(7) + 2log(2x-3)

Answer 2

log[7(2x - 3)²]

 

I hope I interpreted this right.  In the future, use the special characters when post an expression or equation to make the clearer.

 

 

When multiplying arguments, we add the log terms.

 

log7 + log(2x - 3)²

 

 

Any exponents get brought down as the coefficient of the log.

 

log7 + 2log(2x - 3)

Answer 3

log₁₀[7 (2x - 3)²] = log₁₀7 + 2*log₁₀(2x - 3)