Question

Without using tables or calculator solve for x in the equation. Log(2x-11)-Log2=Log3-Log2

Answer 1

Using the properties of logarithms, we can simplify the equation as follows:

Log(2x-11) - Log(2) = Log(3) - Log(2)

Applying the quotient rule of logarithms, we can combine the expressions on the left side:

Log[(2x-11)/2] = Log(3/2)

Since the base of the logarithm is the same on both sides (base 10), we can remove the logarithm:

(2x-11)/2 = 3/2

To solve for x, we can multiply both sides of the equation by 2:

2x - 11 = 3

Now, isolate the x term by adding 11 to both sides:

2x = 14

Finally, divide both sides by 2:

x = 7

Therefore, the solution to the equation is x = 7.