Question

If 322c = 80+7, what is the value of c?

Answer 1

Answer:

c = 3

Step-by-step explanation:

Using the rule of exponents

$(a^m)^{n}$ = $a^{mn}$

note that 32 = $2^{5}$ and 8 = 2³ , then

$32^{2c}$ = $8^{c+7}$ , becomes

$(2^5)^{2c}$ = $(2^3)^{c+7}$

$2^{10c}$ = $2^{3c+21}$

Since the bases on both sides are equal, both 2, then equate the exponents

10c = 3c + 21 ( subtract 3c from both sides )

7c = 21 ( divide both sides by 7 )

c = 3