Question

Find the value of x, if:

$\left(\frac{125}{27}\right)\times (\frac{125}{27}{)}^x=(\frac{5}{3}{)}^{18}$

• A. $5^3$
• B. 5
• C. $5\times 3\times 5$
• D. $3^5$

Answer 1

The correct option is B 5

$\left(\frac{125}{27}\right)\times (\frac{125}{27}{)}^x=(\frac{5}{3}{)}^{18}$

$\Rightarrow \left(\frac{5^3}{3^3}\right)\times (\frac{5^3}{3^3}{)}^x=(\frac{5}{3}{)}^{18}$

$\Rightarrow (\frac{5}{3}{)}^3\times (\frac{5}{3}{)}^{3x}=(\frac{5}{3}{)}^{18}$

⇒ 3 + 3x = 18 [Equating the powers of same base]
3x = 18 – 3 = 15
x = 5