What is the value of $A$ when we rewrite $\left(\frac{5}{2}\right)^{x}+\left(\frac{5}{2}\right)^{x+3}$ as
$$
\begin{array}{l}
A \cdot\left(\frac{5}{2}\right)^{x} ? \
A=\square
\end{array}
$$

Question

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ We start with the expression $ \left( \frac{5}{2} \right)^{x} + \left( \frac{5}{2} \right)^{x+3} $ and rewrite it as $ \left( \frac{5}{2} \right)^{x} \left( 1 + \left( \frac{5}{2} \right)^{3} \right) $. ‖ ‖ step 2 ⋮ Simplifying $ 1 + \left( \frac{5}{2} \right)^{3} $ gives us $ 1 + \frac{125}{8} = \frac{8 + 125}{8} = \frac{133}{8} $. ‖ ‖ step 3 ⋮ Therefore, we can express the original equation as $ \left( \frac{5}{2} \right)^{x} \cdot \frac{133}{8} $. ‖ ‖ step 4 ⋮ To express this in the form $ \left( \frac{5}{2} \right)^{A} $, we need to find $ A $ such that $ A = \log_{\frac{5}{2}} \left( \frac{133}{8} \right) + x $. ‖ ∻Answer∻ ⚹ $ A = x + \log_{\frac{5}{2}} \left( \frac{133}{8} \right) $ ⚹ ∻Key Concept∻ ⚹ Rewriting expressions using properties of exponents and logarithms ⚹ ∻Explanation∻ ⚹ The value of $ A $ is derived from rewriting the sum of two exponential terms into a single term by factoring out the common base and using logarithmic properties. ⚹◊What is the value of $A$ when you factor the expression $\left(\frac{5}{2}\right)^x + \left(\frac{5}{2}\right)^{x+3}$?⍭ Generate me a similar question◊

Sia