For what value of \( x \) is the following true? \( \log (x+8)=\log x+\log 8 \). Your answer is \( x= \) Question Help: Video Submit Question

To solve the equation \( \log (x+8)=\log x+\log 8 \), you can apply the properties of logarithms. Remember that the sum of logarithms can be rewritten as the logarithm of a product: \( \log a + \log b = \log (ab) \). So, the equation transforms to: \[ \log (x+8) = \log (8x) \] Now, if the logarithms are equal, their arguments must also be equal (as long as the arguments are positive), leading to the equation: \[ x + 8 = 8x \] Rearranging gives you: \[ 8 = 8x - x \implies 8 = 7x \implies x = \frac{8}{7} \] So the value of \( x \) is \( \frac{8}{7} \). Therefore, your answer is \( x = \frac{8}{7} \).