write the expression as the logarithm of a single quantity
3[ln x-2 ln(x^2+1)]+2 ln 5
3logx-6log(x^2+1)+log25
logx^3-log(x^2+1)+log25
logx^3+log25-log(x^2+1)^6
log(x^3*25/(x^2+1)^6))
wait, may I ask you what happened to ln?
it is the same thing bro log and ln
ln is log base e
3[ln x-2 ln(x^2+1)]+2 ln 5
ln a - ln b = ln (a/b)
n ln x = ln x^n
so
3 ln [ x/(x^2+1)^2] + ln 25
ln 25[ x/(x^2+1)^2]^3
so agree with Sam
To write the expression as the logarithm of a single quantity, we need to apply logarithmic properties.
Let's break down the expression step by step:
1. Start with the given expression:
3[ln x - 2 ln(x^2 + 1)] + 2 ln 5
2. Apply the logarithmic property: ln(a) - ln(b) = ln(a/b)
This property allows us to combine the two logarithms that are being subtracted.
Applying it to the expression, we get:
3[ln x - ln((x^2 + 1)^2)] + 2 ln 5
3. Now, let's apply another logarithmic property: n ln a = ln(a^n)
This property states that when a coefficient is multiplied with a logarithm, it can be written as the logarithm of the base raised to the power of the coefficient.
Applying it to our expression, we get:
3 ln[x / ((x^2 + 1)^2)] + ln(5^2)
4. Simplifying further, we can write 5^2 as 25:
3 ln[x / ((x^2 + 1)^2)] + ln 25
So, the expression in terms of a single logarithm is:
ln[x / ((x^2 + 1)^2)] + ln 25