Final answer to the problem
$x=\frac{63\ln\left(2\right)-7}{3-1e\ln\left(128\right)}$
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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
Decompose $128$ in it's prime factors
$e^{\left(3x+7\right)}=\left(2^{7}\right)^{\left(ex+9\right)}$
Learn how to solve problems step by step online.
$e^{\left(3x+7\right)}=\left(2^{7}\right)^{\left(ex+9\right)}$
Learn how to solve problems step by step online. Solve the exponential equation e^(3x+7)=128^(ex+9). Decompose 128 in it's prime factors. Simplify \left(2^{7}\right)^{\left(ex+9\right)} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 7 and n equals ex+9. Solve the product 7\left(ex+9\right). We can take out the unknown from the exponent by applying natural logarithm to both sides of the equation.
Final answer to the problem
$x=\frac{63\ln\left(2\right)-7}{3-1e\ln\left(128\right)}$
