How to solve 1n 2 + 1n x = 5.
I read that as
n^2 + n^x = 5
which is an equation with two variables, thus there is no unique solution
e.g. if x = 3, we have n^2 + n^3 = 5
which becomes a cubic equation, with n = appr 1.4334
if n = 2, we have 2^2 + 2^x = 5
2^x = 1
x = 0
clarify what you mean.
It appears you cannot tell the difference between one(1) and L(l). I assume you meant
ln 2 + ln x = 5
recall that lna+lnb = ln(ab). So,
ln(2x) = 5
2x = e^5
x = e^5 / 2
To solve the equation 1n 2 + 1n x = 5, we need to use logarithmic properties.
Step 1: Combine the two logarithms using the logarithmic property of addition. This property states that log(a) + log(b) = log(a * b).
So, the equation becomes 1n (2 * x) = 5.
Step 2: Simplify the equation. Since 1n is the natural logarithm function with base e, we can rewrite it as ln.
Thus, we have ln (2x) = 5.
Step 3: Rewrite the equation in exponential form. This step involves changing the logarithmic equation into exponential form using the property that ln(x) = y is equivalent to e^y = x.
In this case, e^5 = 2x.
Step 4: Solve for x. Divide both sides of the equation by 2:
e^5 / 2 = x.
This is the solution to the equation 1n 2 + 1n x = 5.