Question

Solve the following exponential equations

Answer 1

x = 2, y = - 25

Explanation:

(1)

note that 36 = 6² , then

`6^(x)` = 6²

Since bases on both sides are equal then equate the exponents

x = 2

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(2)

Using the rule of exponents

`(a^m)^(n)` =
`a^(mn)`

note that 25 = 5² , then

`25^(11+3y)` =
`(5^2)^(11+3y)` =
`5^(22+6y)`

Then

`5^(5y-3)` =
`5^(22+6y)`

Since bases on both sides are equal then equate the exponents

22 + 6y = 5y - 3 ( subtract 5y from both sides )

22 + y = - 3 ( subtract 22 from both sides )

y = - 25