helo sir/madam
can u help me to solve this problem
sOLVE 2log 15 +log(5-x)- log4x=2
ROCKSON BEDI
Hello! I'd be happy to help you solve this problem. To begin, let's rewrite the equation using logarithmic properties to simplify it:
2log15 + log(5-x) - log4x = 2
Next, we can apply the rules of logarithms to simplify this equation further:
log15^2 + log(5-x) - log(4x) = 2
Using the logarithmic property log a + log b = log(ab), we can combine the first two terms:
log(15^2 * (5-x)) - log(4x) = 2
Now, we can apply another logarithmic property log a - log b = log(a/b) to combine the last two terms:
log((15^2 * (5-x)) / (4x)) = 2
To solve this equation, we can eliminate the logarithm by taking the exponentiation of both sides using the base 10:
10^log((15^2 * (5-x)) / (4x)) = 10^2
Simplifying further, we have:
(15^2 * (5-x)) / (4x) = 100
Now, let's simplify the equation by distributing 15^2:
(225 * (5-x)) / (4x) = 100
Next, let's cross multiply to get rid of the fractions:
225 * (5-x) = 100 * 4x
Now, we can simplify the equation further by expanding:
1125 - 225x = 400x
Let's move all the variables to one side of the equation:
225x + 400x = 1125
Combining the x terms, we have:
625x = 1125
Now, we can solve for x by dividing both sides of the equation by 625:
x = 1125 / 625
Simplifying, we get:
x = 1.8
So, the solution to the equation 2log15 + log(5-x) - log4x = 2 is x = 1.8.
3 important rules of logs
1. log (AB) = log A + log B
2. log(A/B) = log A - log B
3. log A^n = nlogA
so 2log15 + log(5-x) - log 4x = 2
log 15^2 + log(5-x) - log 4x = 2
log (225(5-x)/(4x) ) = 2
225(5-x)/(4x) = 10^2 = 100
400x = 1125 - 225x
625x = 1125
x = 1125/625 = 9/5 or 1.8