promath The natural log of x is the logarithm of x with base e, and it is denoted by ln(x). That is, logex = lnx. The integral of natural log of x is equal to ∫ln(x) dx = xln(x) -x+C, where C is a constant. Here, we will learn how to find the integration of natural … Read more
The general solution of the differential equation dy/dx+ytanx = secx is equal to ysecx =tanx +C where C is a constant. This equation is an example of a first order linear ordinary differential equation. Solve dy/dx+ytanx = secx Question: Solve the differential equation $\dfrac{dy}{dx}$+ytanx = secx. Solution: The given equation has the form $\dfrac{dy}{dx}+P(x)=Q(x)$, a … Read more
The value of log 81 base 3 is equal to 4. As log 81 base 3 is written as log381, we have that log381 =4. In this post, we will learn how to find the logarithm of 81 with base 3. The formula of the logarithm of 81 with base 3 is given as follows: … Read more
The value of log 81 with base 27 is equal to 4/3. The logarithm of 81 with base 27 is written as log2781, so the formula of log81 base 17 is given by log2781 = 4/3. Value of log 81 base 27 Answer: The value of log 81 base 27 is equal to 4/3, that … Read more
The general solution of the differential equation (x+y+1)dy/dx=1 is equal to x= -(y+2)+Cey where C denotes an arbitrary constant. Here we will learn how to solve the differential equation (x+y+1)dy/dx=1. Solve (x+y+1)dy/dx=1 Question: What is the solution of (x+y+1)$\dfrac{dy}{dx}$=1? Answer: Let us put x+y+1 = v. Differentiating w.r.t x, we get that $1+\dfrac{dy}{dx}=\dfrac{dv}{dx}$ ⇒ $\dfrac{dy}{dx}=\dfrac{dv}{dx}-1$ … Read more
The value of log 2 with base 8 is equal to 1/3. The logarithm of 2 with base 8 is written as log82, so the formula of log2 base 8 is given by log82 = 1/3. Value of log 2 base 8 Answer: The value of log 2 base 8 is equal to 1/3, that … Read more
The derivative of x^lnx (x to the power lnx) is equal to 2xlnx -1 lnx. Here, ln denotes the natural logarithm, that is, lnx =loge x. In this post, we will learn how to differentiate xlnx. What is the Derivative of xlnx? Answer: Explanation: To find the derivative of xlnx, we will use the logarithmic … Read more
The value of log 27 base 3 is equal to 3. Here, we learn to find the logarithm of 27 when the base is 3. The formula of log327 is as follows: log327 = 3. Find log 27 base 3 Answer: The value of log 27 with base 3 is equal to 3, that is, … Read more
The value of log 8 base 2 is equal to 3. Here, we will learn how to find logarithm of 8 with base 2. The formula of log28 is given below: log28 = 3. Value of log 8 base 2 Answer: The value of log 8 with base 2 is equal to 3, that is, … Read more
The general solution of the differential equation dy/dx=x-y is equal to y=x-1-Ce-x where C is an arbitrary constant. In this post, we will learn how to find the general solution of dy/dx =x-y. Solution of dy/dx=x-y Question: Find the genral solution of $\dfrac{dy}{dx}$ =x-y. Solution: Let x-y=v. Differentiating w.r.t x, we get that $1-\dfrac{dy}{dx}=\dfrac{dv}{dx}$ ⇒ … Read more