Question

Given that 2p x 8q = 2n , express n in terms of p and q

Answer 1

`\sf \: p + 3q = n`

Explanation:

`2^p*8^q=2^n`

First, write 8^q as a power of 2.

`2^p*8^q=2^n\\2^p*2^3^q=2^n`

As all the bases are same, exponents are also equal.

Now add the powers.

∴ p + 3q = n

Answer 2

n = p+3q

Explanation:

2^p x 8^q = 2^n

Exponent rules

Rewriting 8 as 2^3

2^p x 2^3^q = 2^n

Using the rule a^b^c = a^(b*c)

2^p x 2^3q = 2^n

Using the rule a^b * a^c = a^(b+c)

2 ^(p+3q) = 2^n

Since the bases are the same, the exponents are the same

p+3q = n