given that equation 2logx +log2= log5+10.solve for x
The last I knew, Kampala was the capital of Uganda, but I'll take your word for it that you are taking it as a School Subject.
http://en.wikipedia.org/wiki/Kampala
2logx + log2 = log5 + 10
log x^2 + log2 = log5 + 10
log x^2 = log5 - log2 + 10
logx^2 = log (5/2) = 10
logx^2 = 10.39794..
x^2 = 10^10.39794..
x = 10^5.19897..
x = appr 158,114
I suspect a typo which would change the order of operation.
my answer works for the equation the way it was typed.
check:
LS = 2log 158114 + log2
= 10.39784... + .301029...
= 10.69897..
RS = log5 + 10
= .69897.. + 10
= 10.69897..
To solve the given equation, we need to use logarithmic rules to simplify it.
The equation is: 2log(x) + log(2) = log(5) + 10.
First, let's apply the power rule of logarithms, which states that log(a^b) = b * log(a):
Rewriting the equation using the power rule:
log(x^2) + log(2) = log(5) + 10.
Next, we can combine the logarithms on the left-hand side using the product rule of logarithms, which states that log(a) + log(b) = log(a * b):
Combining the logarithms:
log(2x^2) = log(5) + 10.
Now, using the properties of logarithms, we can eliminate the logarithm on both sides:
2x^2 = 5 * 10^1.
Simplifying the equation:
2x^2 = 50.
Next, divide both sides of the equation by 2 to isolate x^2:
x^2 = 50/2.
Solving for x^2:
x^2 = 25.
Finally, take the square root of both sides to find the value of x:
x = ±√25.
Therefore, x can be either +5 or -5 as both values of x satisfy the equation.