How do you write a logarithmic function?

Then the logarithmic function is given by; f(x) = log _b x = y, where b is the base, y is the exponent and x is the argument. The function f (x) = log _b x is read as “log base b of x.” Logarithms are useful in mathematics because they enable us to perform calculations with very large numbers.

How do you solve logarithmic equations step by step?

Solving Logarithmic EquationsStep 1: Use the rules of exponents to isolate a logarithmic expression (with the same base) on both sides of the equation.Step 2: Set the arguments equal to each other.Step 3: Solve the resulting equation.Step 4: Check your answers. Solve. Step 1: Use the properties of the logarithm to isolate the log on one side.

What is an example of a logarithmic function?

For example, y = log2 8 can be rewritten as 2y = 8. Since 8 = 23 , we get y = 3. As mentioned in the beginning of this lesson, y represents the exponent, and it also represents the logarithm. Therefore, a logarithm is an exponent.

What is a logarithmic equation?

A logarithmic equation is an equation that involves the logarithm of an expression containing a variable. To solve exponential equations, first see whether you can write both sides of the equation as powers of the same number.

What does a logarithmic equation look like?

The logarithmic function, , is spoken as “the log, base a, of x.” The logarithmic function is the inverse of the exponential function, so one can also think of logarithms by using exponential form. is the same operation as thinking “a to the y power equals x.” The common logarithmic function, written y = log x, has an

How do you solve logarithmic equations with different bases?

How to Solve Logarithms With Different BasesStep 1: Change the Base to 10. Using the change of base formula, you have. Step 2: Solve for the Numerator and Denominator. Since your calculator is equipped to solve base-10 logarithms explicitly, you can quickly find that log 50 = 1.699 and log 2 = 0.3010.Step 3: Divide to Get the Solution. 1.699/0.3010 = 5.644.

Can a logarithmic equation have a negative solution?

Logarithms cannot have non-positive arguments (that is, arguments which are negative or zero), but quadratics and other equations can have negative solutions. Each log in the equation had the same base, and each side of the log equation ended up with the value, so the solution “checks”.