Question

Solve the logarithmic equation. Be sure to reject any value of log (X + 8) = log x + log 8​

Answer 1

`x = (8)/(7)`

Explanation:

`log(x + 8) = log(x) + log(8) \\ (x + 8) = 8x \\ x + 8 = 8x \\ 8 = 8x - x \\ 8 = 7x \\ (8)/(7) = (7x)/(7) \\ x = (8)/(7)`

Answer 2

x = 8/7

Explanation:

log (X + 8) = log x + log 8​

We know that log a + log b = log ab

log (X + 8) = log 8x

Raise each side to base 10

10^log (X + 8) = 10^log 8x

x+8 = 8x

Subtract x from each side​

x+8-x = 8x-x

8 = 7x

Divide by 7

8/7 = 7x/7

8/7 =x