Home > Precalculus > Natural Logs

How do you solve #log_3 6 + log_3x = log_3 12#?

Answer 1

Anna Allen

#x = 2#

If you are adding log terms, it means you can condense them into one log and multiply the numbers

#log_3 6 + log_3 x = log_3 12#

#log_3 (6 xx x) = log_3 12#

#log_3 6x = log_3 12" "larr if log A = log B, hArr A = B#

#6x = 12#

#x = 2#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Chloe Alexander

To solve the equation log₃ 6 + log₃ x = log₃ 12, you can use the properties of logarithms. By applying the product rule of logarithms, you can combine the terms on the left side:

log₃ (6x) = log₃ 12

Since the logarithm functions are equal, their arguments must also be equal:

6x = 12

Now, you can solve for x:

x = 12 / 6 x = 2

By signing up, you agree to our Terms of Service and Privacy Policy

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.