Which term is 13122?
The geometric sequence is 2, -6, 18, -54
tn=ar^(n-1)
13122=2(-3)^(n-1)
6561=(-3)^(n-1)
log6561=n-1log-3
You can't divide with negative logs, how do I isolate n?
To isolate "n" in the equation log6561 = n - 1 log(-3), you need to use a property of logarithms known as the change of base formula. This formula allows you to convert logarithms of any base to logarithms of another base.
The change of base formula states: logₐ(b) = logₓ(b) / logₓ(a), where logₐ(b) represents the logarithm of "b" base "a" and logₓ represents the logarithm of some base "x".
In this case, you want to isolate "n." So, to apply the change of base formula and eliminate the negative logarithm, follow these steps:
Step 1: Rewrite the equation using the change of base formula:
logₓ(6561) = (n - 1) logₓ(-3)
Step 2: Choose a base for the logarithm that is not negative. For simplicity, let's choose base 10:
log(6561) / log(-3) = (n - 1) log(10)
Step 3: Evaluate the logarithms on the left side of the equation:
4 / log(-3) = (n - 1) x 1
4 = n - 1
Step 4: Solve for "n":
n = 4 + 1
n = 5
Therefore, the term corresponding to 13122 in the geometric sequence 2, -6, 18, -54 is the 5th term.