Express p in terms of q and r in the formula r^p+1=1+3q

Answer 1

To express p in terms of q and r in the formula r^(p+1) = 1 + 3q, we can take the logarithm of both sides of the equation.

Taking the logarithm of both sides with base r, we have:
log_r(r^(p+1)) = log_r(1+3q)

Applying the logarithmic property, we can bring down the exponent (p+1) in the left side:
(p+1)log_r(r) = log_r(1+3q)

The logarithm of a number with the same base is 1, so we simplify further:
(p+1)(1) = log_r(1+3q)

Therefore, we have:
p + 1 = log_r(1+3q)

Finally, we rearrange the equation to express p in terms of q and r:
p = log_r(1+3q) - 1