Question

Solve the following exponential equations

Answer 1

Answer:

x = 2, y = - 25

Step-by-step 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