Respuesta :
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. [tex]32^{2c}[/tex]
8 Superscript c + 7 i.e. [tex]8^{c+7}[/tex]
The equation form is [tex]32^{2c}=8^{c+7}[/tex].
Write the expression as,
[tex](2^5)^{2c}=(2^3)^{c+7}[/tex]
[tex](2)^{10c}=(2)^{3c+21}[/tex]
Comparing the base,
[tex]10c=3c+21[/tex]
[tex]10c-3c=21[/tex]
[tex]7c=21[/tex]
[tex]c=\frac{21}{7}[/tex]
[tex]c=3[/tex]
Therefore, the value of c is 3.
So option 3 is correct.
