I need help with a logarithmic equations!!!! ASAP!!!!!

Question

log₄(2x+1)+1=log₄(x+5)

how do I get rid of the plus one? I need a step by step please!!

Answer 1

log₄(2x+1)+1=log₄(x+5)

1 = log₄ 4

log₄ (2X +1) + log₄ 4 = log₄(X+5) sum of logs = log of products

log₄ (4 * (2X+1)) = log₄(X+5) take antilogs (if the logs of two expressions are equal, the expressions must be equal)

4 * (2X+1) = (X+5) Solve for X

X = 1/7

Answer 2

1 = log₄(4)

Thus, we have

log₄(2x+1) + log₄(4) = log₄(x+5)

The sum of logs equals the log of their product.

log₄[(2x+1) (4)] = log₄(x+5)

Thus, we set the two terms, which are both to the log₄, equal.

(If you prefer, calculate 4 to the power of both sides to remove the log)

Then, (2x+1)(4) = x+5

8x+4 = x + 5

7x = 1

x = 1/7

Note that x+5 and 2x+1 are positive. Thus, there are no issues with taking the log.