solve algerbraically for x

log27(2x-1)=4/3

I did
2x-1=27(4/3)
2x-1=3^4
2x=82
I got x=41
does this look right?
thank you

correct.

Yes

To solve the equation logarithmically for x, you followed the right steps until you reached 2x = 82. However, you made a small error when dividing both sides by 2.

The correct step would be:

2x - 1 = 3^4
2x = 3^4 + 1
2x = 82

Now, divide both sides by 2 to isolate x:

2x/2 = 82/2
x = 41

So, the correct solution is x = 41. Well done!