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

Answer:

$\frac{\ln(2x + 5)}{\ln(x - 3)}$ = 0

Step-by-step 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

$\ln(\frac{A}{B}) = \ln(A)-\ln(B)$

therefore,

we get

$\frac{\ln(2x + 5)}{\ln(x - 3)}$ = 0

Hence,

Expression as the logarithm of a single quantity is $\frac{\ln(2x + 5)}{\ln(x - 3)}$ = 0

Answer 2

Simplify the logarithm.

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

Use the quotient rule [ $\text{ln}\frac{a}{b} = \text{ln(a)}-\text{ln(b)}$ ] 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!