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6^((x-3)/4)=√(6)

Ok, Let’s start by changing the notation to:
6^((x-3)/4) = 6^(1/2)
Then let’s take the log of both sides (I’m just going to take natural log {ln})
ln(6)^(x-3/4) = ln(6)^(1/2)
Because of the properties of logs, you can move the exponent down to be a coefficient:
((x-3)/4)*ln(6) = (1/2)*ln(6)
Then you can divide both sides by ln(6):
((x-3)/4) = (1/2)
Then multiply both sides by 4:
x-3 = 2
Add add three to both side:
x = 5

So the answer is x = 5. Let’s check by plugging it back into the equation:
6^((x-3)/4)= (6)^(1/2)
6^(((5)-3)/4)= (6)^(1/2)
6^(2/4)= (6)^(1/2)
6^(1/2)= (6)^(1/2)