Question

Condensing Logarithmic Expressions In Exercise, use the properties of logarithms to rewrite the expression as the logarithm of a single quantity.

In(2x + 5) = In(x - 3)

Answer 1

Simplify the logarithm.

In(2x + 5) = In(x - 3) → In(2x + 5) - In(x - 3) = 0

Use the quotient rule [
`\text{ln}(a)/(b) = \text{ln(a)}-\text{ln(b)}` ] to simplify.

In(2x + 5) - In(x - 3) = 0 →
`\frac{\text{ln(2x + 5)}}{\text{ln}(x - 3)}=0`

Therefore, the logarithm as a single quantity is
`\frac{\text{ln(2x + 5)}}{\text{ln}(x - 3)}=0`

Best of Luck!

Answer 2

`(\ln(2x + 5))/(\ln(x - 3))` = 0

Explanation:

Data provided in the question:

In(2x + 5) = In(x - 3)

we can rearrange the above equation as

⇒ In(2x + 5) - In(x - 3) = 0

now,

from the properties of natural log function, we know that

`\ln((A)/(B)) = \ln(A)-\ln(B)`

therefore,

we get

`(\ln(2x + 5))/(\ln(x - 3))` = 0

Hence,

Expression as the logarithm of a single quantity is
`(\ln(2x + 5))/(\ln(x - 3))` = 0