How is the graph y=log(2x)+3 related to the graph of y=log(x)

The graph y = log (2x) + 3 is the translation of the graph y = log (x) as much as (3 + log (2)) ≈ 3.3 units up

Further explanation

Function is a relation which each member of the domain is mapped onto exactly one member of the codomain.

There are many types of functions in mathematics such as:

Linear Function → f(x) = ax + bQuadratic Function → f(x) = ax² + bx + cTrigonometric Function → f(x) = sin x or f(x) = cos x or f(x) = tan xLogarithmic function → f(x) = ln xPolynomial function → f(x) = axⁿ + bxⁿ⁻¹ + ...

If function f : x → y , then inverse function f⁻¹ : y → x

Let us tackle the problem.

The given functions can be modified as follows:

From the function above it can be concluded that the graph y = log (2x) + 3 is the translation of the graph y = log (x) as much as (3 + log (2)) ≈ 3.3 units up

To be clearer, it can be seen in the attached image.

Learn moreInverse of Function : Rate of Change : Graph of Function : Answer details

Grade: Middle School

Subject: Mathematics

Chapter: Functions

Keywords: Equation , Line , Variable , Line , Gradient , Point , Quadratic , Intersection , Logarithmic

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With a continuous thought process.