How do you solve #5=6^(3t-1)# ?

Answer 1

Eva Adamson

#t = 1/3((log 5)/(log 6)+1)#

Using the logs from both sides, we get:

#log 5 = log (6^(3t-1)) = (3t-1) log 6#

Divide both ends by #log 6# and transpose to get:

#3t - 1 = (log 5)/(log 6)#

Add #1# to both sides to get:

#3t = (log 5)/(log 6) + 1#

Divide both sides by #3# to get:

#t = 1/3((log 5)/(log 6)+1)#

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Answer 2

Kennedy Adams

To solve the equation (5 = 6^{3t-1}), you can follow these steps:

Take the logarithm of both sides of the equation.
Use the properties of logarithms to simplify the equation.
Solve for (t) by isolating it on one side of the equation.

Applying these steps:

[\log(5) = \log(6^{3t-1})]

Using the property (\log(a^b) = b\log(a)):

[\log(5) = (3t-1)\log(6)]

Now, solve for (t):

[3t-1 = \frac{\log(5)}{\log(6)}]

[3t = \frac{\log(5)}{\log(6)} + 1]

[t = \frac{1}{3}\left(\frac{\log(5)}{\log(6)} + 1\right)]

This is the solution for (t).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.