Question

Marta simplified this expression.

4 logs x+logs 2x log, 3x
In which step did she incorrectly apply a property of logarithms?

Answer 1

step 1

Explanation:

You want to know which step in Marta's simplification of 4·log₅(x) +log₅(2x) -log₅(3x) contains an error in application of properties of logarithms.

Properties of logs

log(a^b) = b·log(a)

log(ab) = log(a) +log(b)

log(a/b) = log(a) -log(b)

Simplification

`4\log_5(x)+\log_5(2x)-\log_5(3x)\\\\=\log_5(x^4)+\log_5(2x)-\log_5(3x)\qquad\text{Step 1. Mistake: $4x$ instead of $x^4$}\\\\\log_5(x^4\cdot2x)-\log_5(3x)=\log_5\left((2x^5)/(3x)\right)\\\\=\boxed{\log_5\left((2x^4)/(3)\right)}`