For what value of $$ x $$ is the following true? $$ \log (x+8)=\log x+\log 8 $$. Your answer is $$ x=\square $$

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Solve the equation $$ \log(x+8)=\log(x)+\log(8) $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\log_{10}{\left(x+8ight)}=\log_{10}{\left(xight)}+\log_{10}{\left(8ight)}$$
- step1: Find the domain:
  $$\log_{10}{\left(x+8ight)}=\log_{10}{\left(xight)}+\log_{10}{\left(8ight)},x>0$$
- step2: Simplify:
  $$\log_{10}{\left(x+8ight)}=\log_{10}{\left(xight)}+3\log_{10}{\left(2ight)}$$
- step3: Add or subtract both sides:
  $$\log_{10}{\left(x+8ight)}-\left(\log_{10}{\left(xight)}+3\log_{10}{\left(2ight)}ight)=0$$
- step4: Subtract the terms:
  $$\log_{10}{\left(\frac{x+8}{x}ight)}-3\log_{10}{\left(2ight)}=0$$
- step5: Move the constant to the right side:
  $$\log_{10}{\left(\frac{x+8}{x}ight)}=0+3\log_{10}{\left(2ight)}$$
- step6: Add the terms:
  $$\log_{10}{\left(\frac{x+8}{x}ight)}=3\log_{10}{\left(2ight)}$$
- step7: Evaluate the logarithm:
  $$\frac{x+8}{x}=2^{3}$$
- step8: Cross multiply:
  $$x+8=x	imes 2^{3}$$
- step9: Simplify the equation:
  $$x+8=2^{3}x$$
- step10: Move the variable to the left side:
  $$x+8-2^{3}x=0$$
- step11: Calculate:
  $$-7x+8=0$$
- step12: Move the constant to the right side:
  $$-7x=0-8$$
- step13: Remove 0:
  $$-7x=-8$$
- step14: Change the signs:
  $$7x=8$$
- step15: Divide both sides:
  $$\frac{7x}{7}=\frac{8}{7}$$
- step16: Divide the numbers:
  $$x=\frac{8}{7}$$
- step17: Check if the solution is in the defined range:
  $$x=\frac{8}{7},x>0$$
- step18: Find the intersection:
  $$x=\frac{8}{7}$$
The value of $$ x $$ for which the equation $$ \log (x+8) = \log x + \log 8 $$ is true is $$ x = \frac{8}{7} $$ or $$ x = 1.142857 $$ (rounded to 5 decimal places).
$$ x = \frac{8}{7} $$

For what value of \( x \) is the following true? \( \log (x+8)=\log x+\log 8 \). Your answer is \( x=\square \)

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