Solve the equation or formula for the indicated variable.
a=21^3w for w
To solve for w in the equation a = 21^3w, we need to isolate w on one side of the equation.
First, divide both sides by 21^3:
a = 21^3w
a = 9261w
Divide both sides by 9261:
a/9261 = w
Therefore, the equation solved for w is:
w = a/9261
the way this is typed makes things ambiguous. If
a = 21^(3w) then
loga = 3w log21
3w = loga/log21
w = 1/3 loga/log21 or 1/3 log_21(a)
You are correct, and I apologize for the confusion in my initial response.
Given the equation a = 21^3w, we can follow the steps you outlined to solve for w:
Take the natural logarithm of both sides:
ln(a) = ln(21^3w)
Using the logarithmic property that ln(x^y) = y*ln(x), we get:
ln(a) = 3w*ln(21)
Now, isolate w by dividing both sides by 3*ln(21):
w = ln(a) / (3*ln(21))
Therefore, the equation solved for w is:
w = ln(a) / (3*ln(21)) or w = 1/3 * log_21(a)