Logv3(12) = logv3 (3t^2) - logv3 (3t)
(the v means "log 3"- 3 is the base)
remember to divide the terms when subtracting in logarithms.
WAIT ITS t^2 NOT 3t^2
ok, divide throughout by logv3 and then you will get a quadratic equation and solve for t.
But then when i try to factor i get 0=t^2-3t-12
Complete the square method.
To solve the given equation, we can use the properties of logarithms.
First, let's simplify the right side of the equation using the properties of logarithms.
Using the quotient rule of logarithms, we can rewrite the right side of the equation as a single logarithm:
logv3 (3t^2) - logv3 (3t) = logv3 [(3t^2)/(3t)]
Next, simplify the expression inside the logarithm:
logv3 [(3t^2)/(3t)] = logv3 (t)
Now, the equation becomes:
Logv3(12) = logv3 (t)
Since the bases are the same (logv3), we can set the arguments equal to each other:
12 = t
Therefore, the solution to the equation is t = 12.
In summary, we simplifed the equation using the properties of logarithms and set the arguments equal to each other to solve for the unknown variable (t).