how do you Solve 2log x-log 3=2
pls help
2 log x - log 3 = 2
recall some laws of exponents. Note that we can rewrite the first terms as:
2 log x = log (x^2)
Also, when two log terms of the same base are being subtracted, we can rewrite it as the quotient of the terms inside the log:
log (x^2) - log (3) = log [(x^2)/3]
rewriting the equation,
log (x^2)/3 = 2
we raise both sides by 10 (the base of the log) to cancel the log:
x^2 / 3 = 10^2
x^2 = 300
x = sqrt(300) = +/- 10*sqrt(3)
There are two values of x. But note that we only choose the positive value since we cannot take the log of a negative number (if we substitute back the value of x to the original equation)
Thus, x = 10*sqrt(3)
hope this helps~ :)
yeah it helped. thanks :)
To solve the equation 2log x - log 3 = 2, we can use logarithmic properties and algebraic manipulations.
Step 1: Combine the logs using the property log(a) - log(b) = log(a/b):
2log(x) - log(3) = 2
log(x^2) - log(3) = 2
Step 2: Apply the property log(a) - log(b) = log(a/b) to simplify further:
log(x^2/3) = 2
Step 3: Remove the logarithm by exponentiating both sides of the equation. The base of the logarithm is usually 10 or e (natural logarithm). In this case, we'll use base 10:
10^(log(x^2/3)) = 10^2
Step 4: Simplify by applying the exponentiation property:
x^2/3 = 100
Step 5: Multiply both sides of the equation by 3 to isolate the variable x:
x^2 = 300
Step 6: Take the square root of both sides to solve for x:
x = ±√300
Step 7: Simplify the square root of 300:
x ≈ ±17.32
Therefore, the solutions to the equation 2log x - log 3 = 2 are approximately x ≈ -17.32 and x ≈ 17.32.