The graph is wrong and can be subject to misinterpretation as the values in the graph don't add up to 100
63+80+70 is equal to 213
2x+6 is the base
Then the equation is logarithm of 144 on basis 2x + 6 = 2
Then [2x + 6]^2 = 144
Now expand the square binomial
4x^2 + 24x + 36 = 144
4x^2 + 24x + 36 - 144 = 0
4x^2 + 24x - 108 = 0
Divide by 4
x^2 + 6x - 27 = 0
Factor: (x + 9 ) (x - 3) = 0
x = -9 and x = 3
The only valid is x = 3, because x = -9 yields 2x + 6 = - 12 and the logarithm function cannot have negative basis.
Then the answer is x = 3.
In the given problem there are several known and important facts to take note of. Firstly the restaurant bill without tax and tips is $28.35. Then the tax of 6.25% needs to be added with the bill. Also a tip of 20% on the original bill needs to be added to find the total cost.
Then tax on the restaurant bill = (6.25/100) * 28.35
= 1.77
So the tax on the restaurant bill is $1.77
Amount of tips given = 28.35 * (20/100)
= 5.67
Amount of tips paid is $5.67
Total cost paid in the restaurant = ( 28.35 + 1.77 + 5.67) dollars
= 35.79 dollars
