Answer: x = 5
Explanation:
We can use the logarithm properties to help us solve. These are all common logarithms, are logarithms with base 10, so we can use these properties. We will use the addition property and the one-to-one property.
Given:
log (2x – 3) + log 8 = log (9x + 11)
Addition property for logarithms:
log ((2x – 3) * 8) = log (9x + 11)
Simplify by distribution:
log (16x – 24) = log (9x + 11)
One-to-one property:
16x – 24 = 9x + 11
Add 24 to both sides of the equation and subtract 9x from both sides:
16x – 9x – 24 + 24 = 9x – 9x + 11 + 24
7x = 35
Divide both sides of the equation by 7:
x = 5