9⁴ = 9ˣ ((2³)⁵)⁷ = 2ˣ 10² · √(10⁵) = √(10ˣ)...

Questions

September 2022 1 0 Report

55 point quiz from kexcvi:
Find the value of x in the following questions!
3² · 3⁵ = 3ˣ
9¹² / 9⁴ = 9ˣ
((2³)⁵)⁷ = 2ˣ
10² · √(10⁵) = √(10ˣ)

Answers & Comments

EngrJohann

Verified answer

$\large \color{white}\mathcal\colorbox{blue}{SOLUTION:}$

$\begin{array}{l} \begin{aligned} 1.)\: \sf 3^2 \cdot 3^5 &=\sf 3^x \\ \\ \sf 3^{2 + 5} &=\sf 3^x \\ \\ \sf 3^7 &= \sf 3^x \end{aligned} \\ \\ \:\: \implies \boxed{\sf x = 7} \\ \\ \\ \begin{aligned} 2.)\: \quad \sf \dfrac{9^{12}}{9^4} &=\sf 9^x \\ \\ \sf 9^{12 - 4} &=\sf 9^x \\ \\ \sf 9^8 &= \sf 9^x \end{aligned} \\ \\ \quad\!\implies \boxed{\sf x = 8} \\ \\ \\ \begin{aligned} 3.)\: \sf {\bigg({\big(2^3\big)}^5\bigg)}^7 &= \sf 2^x \\ \\ \sf 2^{3(5)(7)} &=\sf 2^x \\ \\ \sf 2^{105} &= \sf2^x \end{aligned} \\ \\ \quad \quad \implies \boxed{\sf x = 105} \\ \\ \\ \begin{aligned} 4.)\: \sf 10^2 \cdot \sqrt{10^5} &= \sf \sqrt{10^x} \\ \\ \sf 10^{2 + \frac{5}{2}} &= \sf 10^{\frac{x}{2}} \\ \\ \sf 10^{\frac{9}{2}} &= \sf 10^{\frac{x}{2}} \\ \\ \sf \dfrac{9}{2} &= \sf \dfrac{x}{2} \end{aligned} \\ \\ \:\:\qquad \implies \boxed{\sf x = 9} \end{array}$