Question

(1/6)^p = 36^3 * 6^18

What is the value of p?
Can someone answer this by taking the square root of p, rather than using logarithms? Because I'm in 8th grade so like....we haven't learned log and the big exam is today and idk what to do with this problem.

Answer 1

p=-24

Explanation:

The given expression is:

`((1)/(6))^p=36^3*6^(18)`

We express everything to base 6.

`(6)^(-p)=6^(2*3)*6^(18)`

`(6)^(-p)=6^(6)*6^(18)`

Use the product rule:
`a^m*a^n=a^(m+n)`

`(6)^(-p)=6^(6+18)`

`(6)^(-p)=6^(24)`

The bases are the same so we equate the exponents.

`-p=24`

p=-24