Without using tables or calculator solve for x in the equation. Log(2x-11)-Log2=Log3-Log2
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.
To solve for x in the equation log(2x-11) - log2 = log3 - log2, we can use the properties of logarithms. This specific equation can be solved by applying the quotient property of logarithms, which states that log(a) - log(b) = log(a/b).
First, let's simplify the equation using the quotient property:
log((2x-11)/2) = log(3/2)
Now, we can simplify it further by removing the logarithms:
(2x-11)/2 = 3/2
To isolate x, we can multiply both sides of the equation by 2:
2 * (2x-11)/2 = 2 * 3/2
(2x-11) = 3
Next, let's solve for x by getting rid of the -11 on the left side of the equation:
2x - 11 + 11 = 3 + 11
2x = 14
Finally, divide both sides of the equation by 2 to solve for x:
2x/2 = 14/2
x = 7
Therefore, x = 7 is the solution to the equation log(2x-11) - log2 = log3 - log2.