Question

Solve the equation $2^{3x+5}=128$. Check your solution.

Short answer

The solution for the equation is $x=\frac{2}{3}$.

Step-by-step solution

Step 1. Write down the given equation.

The given equation is $2^{3x+5}=128$.

Step 2. Simplify the equation.

The given equation $2^{3x+5}=128$is solved as:

$\begin{array}{l}{2}^{3x+5}=\mathrm{128....}\left(\text{Given}\right)\\ {\left(2\right)}^{3x+5}={\left(2\right)}^7\\ 3x+5=7\\ x=\frac{2}{3}\end{array}$

Step 3. Verify the result for obtained value.

Plugging $x=\frac{2}{3}$in given equation and verify the result.

$\begin{array}{l}{2}^{3x+5}=\mathrm{128....}\left(\text{Given}\right)\\ 2^{3\times \left(\frac{2}{3}\right)+5}=128\\ 2^7=\mathrm{128....}\left(\text{True}\right)\end{array}$

Hence the solution is verified for $x=\frac{2}{3}$.

Step 4. Conclusion.

The solution for the given equation is $x=\frac{2}{3}$.