How do you solve (¼)log_6 (a – 3) – log_6 3 = 0?

1 Answer
Gió
Jun 5, 2016

I found: a=84

Explanation:

We can first get rid of 1/4:
log_6(a-3)^(1/4)-log_6(3)=0
Then we change the subtraction operating on the arguments:
log_6[(a-3)^(1/4)/3]=0
We use the definition of log:
(a-3)^(1/4)/3=6^0
(a-3)^(1/4)/3=1
rearrange:
(a-3)^(1/4)=3
take the power of 4 on both sides:
(a-3)^(1/4*4)=3^4
a-3=81
a=84

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