logx+logx+n-logx/n.plz solve with explanation thanks
Nothing to solve, I don't see an equation
Are you simplifying?
Do you mean
log x + log(x+n) - log(x/n) ???
Do you know your basic rules of logs ?
if so, then
log x + log(x+n) - log(x/n)
= log( x(x+n)) - (logx - logn)
= log( x(x+n) - logx + logn
= log( x(x+n)(n)/x)
= log( n(x+n) )
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To solve the given equation, we will apply the properties of logarithms. Let's break down each term step by step:
1. log(x) + log(x): According to the product rule of logarithms, when adding logarithms with the same base, we can combine them by multiplying the values inside the logarithms. Therefore, log(x) + log(x) = log(x * x) = log(x^2).
2. log(x^2) + n: Here, we have a sum of log(x^2) and n. Since they have different bases, we cannot combine them any further.
3. log(x^2) + n - log(x): Likewise, we cannot combine the terms with different bases, so the equation remains the same.
4. log(x^2) + n - log(x)/n: Now, we can divide log(x) by n since they have the same base. We can use the quotient rule of logarithms, which states that log(a) - log(b) = log(a/b). Applying this rule, we get log(x^2) + n - log(x)/n = log(x^2/x)/n.
Finally, log(x^2/x)/n simplifies further. The division of x^2 by x results in x, so log(x^2/x)/n becomes log(x)/n.
Hence, the given equation, log(x) + log(x) + n - log(x)/n, simplifies to log(x)/n.