Final answer to the problem
$x=-6,\:x=-9$
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Step-by-step Solution
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- Find the derivative using the definition
- Solve by quadratic formula (general formula)
- Simplify
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- Factor by completing the square
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1
Decompose $125$ in it's prime factors
Learn how to solve exponential equations problems step by step online.
$\left(5^{3}\right)^{\left(6-5x\right)}=5^{\left(x^2+72\right)}$
Learn how to solve exponential equations problems step by step online. Solve the exponential equation 125^(6-5x)=5^(x^2+72). Decompose 125 in it's prime factors. Simplify \left(5^{3}\right)^{\left(6-5x\right)} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 3 and n equals 6-5x. If the bases are the same, then the exponents must be equal to each other. Solve the product 3\left(6-5x\right).
Final answer to the problem
$x=-6,\:x=-9$
