Final answer to the problem
$x=5$
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Step-by-step Solution
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- 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
Decompose $25$ in it's prime factors
$\left(5^{2}\right)^{\left(x+1\right)}=125^{\left(x-1\right)}$
Learn how to solve exponential equations problems step by step online.
$\left(5^{2}\right)^{\left(x+1\right)}=125^{\left(x-1\right)}$
Learn how to solve exponential equations problems step by step online. Solve the exponential equation 25^(x+1)=125^(x-1). Decompose 25 in it's prime factors. Simplify \left(5^{2}\right)^{\left(x+1\right)} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals x+1. Rewrite the power 125^{\left(x-1\right)} with base 5. Simplify \left(5^{3}\right)^{\left(x-1\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 x-1.
Final answer to the problem
$x=5$
