Practice Another Solve the following equation analytically. (Enter your answers as a comma-separated list. $$ \begin{array}{l} -\log (x)=6.5 \ x=\square \end{array} $$

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Solve the equation $$ -\log(x)=6.5 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$-\log_{10}{\left(xight)}=6.5$$
- step1: Find the domain:
  $$-\log_{10}{\left(xight)}=6.5,x>0$$
- step2: Simplify:
  $$\log_{10}{\left(xight)}=-6.5$$
- step3: Convert the logarithm into exponential form:
  $$x=10^{-6.5}$$
- step4: Evaluate the power:
  $$x=\frac{1}{10^{\frac{13}{2}}}$$
- step5: Transform the expression:
  $$x=\frac{\sqrt{10}}{10^{7}}$$
- step6: Check if the solution is in the defined range:
  $$x=\frac{\sqrt{10}}{10^{7}},x>0$$
- step7: Find the intersection:
  $$x=\frac{\sqrt{10}}{10^{7}}$$
The solution to the equation $$-\log(x) = 6.5$$ is $$x = \frac{\sqrt{10}}{10^7}$$ or approximately $$3.162278 	imes 10^{-7}$$.
$$ x = \frac{\sqrt{10}}{10^7} $$ or approximately $$ 3.162278 	imes 10^{-7} $$.

Practice Another

Solve the following equation analytically. (Enter your answers as a comma-separated list.

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