Question

Solve the equation 32^× . 25^× = 15^× + ^2 without using calculator.​

Answer 1

Step-by-step explanation:

$\frac{( {32}^{x} \times {25}^{x})} { {15}^{x} } = {15}^{2}$

When you multiply two variables or numbers or with different bases but with the same exponent, you can simply multiply the bases and use the same exponent. For example:

x^a*y^a= (xy)^a

${ (\frac{32 \times 25}{15} })^{x} = {15}^{2}$

${ (\frac{32 \times 5}{3} })^{x} = {15}^{2}$

${ (\frac{160}{3} })^{x} = 225$

x= log (225) ÷ log ( 160/3)