Solve for x

a) 5^(2x) ÷ 5^(7) = 5^3
b)3^(2x)*9=27​

2 thoughts on “Solve for x<br /><br />a) 5^(2x) ÷ 5^(7) = 5^3<br />b)3^(2x)*9=27​”

1. Answer:

   Step-by-step explanation:

   a) 5^(2x )÷ 5^(7) = 5^3

   5^(2x )/5^(7) = 5^3

   5^(2x ) = 5^3 × 5^7

   5^(2x ) = 5^(3 +7) [ bases are equal then powers should be add ]

   5^(2x ) = 5^10

   2x = 10 [bases are equal then powers should be equal ]

   x = 10/2

   x = 5.

   b) 3^(2x )× 9 = 27

   3^(2x ) × 3^2 = 3^3

   3^(2x ) = 3^3 / 3^2

   3^(2x ) = 3^3 × 3^(-2) [1/a = a^(-1)]

   3^(2x ) = 3^(3-2) [ bases are equal then powers should be add ]

   3^(2x ) = 3^1

   2x = 1 [ bases are equal then powers should be equal ]

   x = 1/2.

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2. Answer:

   a) 2x = log (base of 5 ) (5^3 * 5^7)

   b) 2x * 9 = log (base of 3) (27)

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