Final answer to the problem
$x=-50\log_{6}\left(2\right)+50$
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Step-by-step Solution
How should I solve this problem?
- Choose an option
- Solve for x
- Find the derivative using the definition
- Solve by quadratic formula (general formula)
- Simplify
- Find the integral
- Find the derivative
- Factor
- Factor by completing the square
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1
We can take out the unknown from the exponent by applying logarithms in base $10$ to both sides of the equation
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$\log_{6}\left(6^{\left(50-x\right)}\right)=\log_{6}\left(2^{50}\right)$
Learn how to solve problems step by step online. Solve the exponential equation 6^(50-x)=2^50. We can take out the unknown from the exponent by applying logarithms in base 10 to both sides of the equation. Use the following rule for logarithms: \log_b(b^k)=k. Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). We need to isolate the dependent variable x, we can do that by simultaneously subtracting 50 from both sides of the equation.
Final answer to the problem
$x=-50\log_{6}\left(2\right)+50$
Exact Numeric Answer
$x=30.6573596$
