### Solve the exponential equation 3^x = 81 by expressing each side as a power of the same base and then equating exponents.

The main objective of this question is to solve the exponential equation. This question uses the concept of exponential equation. Powers can simply be expressed in concise form using exponential expressions. The exponent shows how frequently the base is utilized as a factor. Expert Answer We are given: [space 3^x space = space 81 ] […]

### Find the linearization L(x) of the function at a.

– $f(x) space = space sqrt ( x ) space , space a space = space 4$ The main objective of this question is to find the linearization of the given function. This question uses the concept of linearization of a function. Determining the linear approximation of a function at a specific location […]

### What is the absolute value of 4i.

The main objective of this question is to find the absolute value for the given expression, which is: [space 4i ] This question uses the concept of Cartesian coordinate system. In a plane, a Cartesian coordinate is a method to describe each point with a unique pair of numbers. These numbers are indeed the signed […]

### Fill in the blank with a number to make the expression a perfect square.

– $dfrac{ x^4 space + space 6 }{ x^5 space + space 7x^3 }$ – $dfrac{ 2 }{ (x^2 space – space 9)^2 }$ The main objective of this question is to find the partial fraction decomposition for the given expressions. This question uses the concept of partial fraction decomposition. Finding antiderivatives of […]