log 2 (x+2) + log 2 5=4 solve logarithmic equations containing both logs and numbers

Question

solve logarithmic equations containing both logs and numbers

1. log₂ (x+2) + log₂ 5=4
2. log₄ x - log ₄ (x-1)= 1/2
3. log ₃ x + log₃ ( x-8)=2
4. log ₄ ( 2x+1) - log₄ ( x-2) =1

Answer 1

Product Property

log₂ (x+2) + log₂ 5 = 4 ------> log₂ (5x+10) = 4

Convert to exponential form

2^4 = 5x + 10 ------> 5x = 16 - 10

5x = 6

x = 6/5 or 1.2