Solve for the variable, round to 4 decimal places. $$ 8^{4 v}+3=83 $$

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Solve the equation $$ 8^{4v}+3=83 $$.
Solve the equation by following steps:
- step0: Solve for $$v$$:
  $$8^{4v}+3=83$$
- step1: Move the constant to the right side:
  $$8^{4v}=83-3$$
- step2: Subtract the numbers:
  $$8^{4v}=80$$
- step3: Take the logarithm of both sides:
  $$\log_{8}{\left(8^{4v}\right)}=\log_{8}{\left(80\right)}$$
- step4: Evaluate the logarithm:
  $$4v=\log_{8}{\left(80\right)}$$
- step5: Divide both sides:
  $$\frac{4v}{4}=\frac{\log_{8}{\left(80\right)}}{4}$$
- step6: Divide the numbers:
  $$v=\frac{\log_{8}{\left(80\right)}}{4}$$
- step7: Simplify:
  $$v=\frac{3+\log_{2}{\left(10\right)}}{12}$$
- step8: Calculate:
  $$v=\frac{4+\log_{2}{\left(5\right)}}{12}$$
The solution to the equation $$8^{4v}+3=83$$ is $$v \approx 0.5268$$ when rounded to 4 decimal places.
$$ v \approx 0.5268 $$

Solve for the variable, round to 4 decimal places.

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