Final answer to the problem
$x=\sqrt{\log_{38}\left(2048\cdot 19^{11}\right)+5},\:x=-\sqrt{\log_{38}\left(2048\cdot 19^{11}\right)+5}$
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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
- Find the roots
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1
Calculate the power $2^{11}$
$38^{\left(x^2-5\right)}=2048\cdot 19^{11}$
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$38^{\left(x^2-5\right)}=2048\cdot 19^{11}$
Learn how to solve problems step by step online. Solve the exponential equation 38^(x^2-5)=2^1119^11. Calculate the power 2^{11}. 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. We need to isolate the dependent variable x, we can do that by simultaneously subtracting -5 from both sides of the equation.
Final answer to the problem
$x=\sqrt{\log_{38}\left(2048\cdot 19^{11}\right)+5},\:x=-\sqrt{\log_{38}\left(2048\cdot 19^{11}\right)+5}$
