Express p in terms of q and r in the formula r^p+1=1+3q
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
To express p in terms of q and r in the formula r^(p+1) = 1 + 3q, we will follow these steps:
Step 1: Subtract 1 from both sides of the equation to isolate the exponent:
r^(p+1) - 1 = 3q
Step 2: Divide both sides of the equation by 3 to isolate q:
(r^(p+1) - 1) / 3 = q
Step 3: Rearrange the equation to solve for p:
p + 1 = log(base r) (3q + 1)/3
Step 4: Subtract 1 from both sides to solve for p:
p = log(base r) (3q + 1)/3 - 1
Therefore, p can be expressed in terms of q and r as p = log(base r) (3q + 1)/3 - 1.