log50+log(x/2)=2
when you add logs, you multiply.
log a + log b = log (a b)
so
log 25 x = 2
by definition if base b log (you did not say if base 10 or base e or base 596 or whatever so I will assume base 10
base^log a = a
so 10^25 x = 25 x
and 10^2 = 100
so
25 x = 100
and
x = 4
To solve the equation log50 + log(x/2) = 2, we can use logarithmic properties and algebraic manipulation.
The equation log50 + log(x/2) = 2 involves the addition of logarithms, which can be simplified using logarithmic rules.
First, we can combine the logarithms using the product rule of logarithms:
log50 + log(x/2) = log(50 * (x/2))
Next, we can simplify the expression inside the logarithm:
log(50 * (x/2)) = log((50x) / 2) = log(25x)
Now, we have the equation log(25x) = 2.
To solve for x, we need to eliminate the logarithm. With a logarithmic equation, we can rewrite it in exponential form using the base of the logarithm. In this case, the base is 10:
10^log(25x) = 10^2
Since the logarithm and the exponential function are inverse operations, they cancel each other out:
25x = 10^2
Now, we can solve for x by simplifying the right side of the equation:
25x = 100
To isolate x, divide both sides of the equation by 25:
x = 100/25
Simplifying further:
x = 4
Therefore, the solution to the equation log50 + log(x/2) = 2 is x = 4.