Question

If 32 Superscript 2 c Baseline = 8 Superscript c + 7, what is the value of c? 1 2 3 5

Answer 1

Answer:

Option 3 - The value of c is 3.

Step-by-step explanation:

Given : If 32 Superscript 2 c Baseline = 8 Superscript c + 7.

To find : What is the value of c?

Solution :

Superscript denotes the power.

32 Superscript 2 c i.e. $32^{2c}$

8 Superscript c + 7 i.e. $8^{c+7}$

The equation form is $32^{2c}=8^{c+7}$.

Write the expression as,

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

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

Comparing the base,

$10c=3c+21$

$10c-3c=21$

$7c=21$

$c=\frac{21}{7}$

$c=3$

Therefore, the value of c is 3.

So option 3 is correct.