Solving and Graphing Exponential Equations - Math

To find the x-intercepts, set the numerator equal to zero.

To find the -intercept, set in the equation and solve.

To find the -intercept(s) of , we need to set the numerator equal to zero.

That means .

The best way to solve for a funky equation like this is to graph it in your calculator and calculate the roots. The result is .

To find the -intercept(s) of , we need to set the numerator equal to zero and solve.

First, notice that can be factored into . Now set that equal to zero: .

Since we have two sets in parentheses, there are two separate values that can cause our equation to equal zero: one where and one where .

Solve for each value:

and

.

Therefore there are two -interecpts: and .

To find the -intercept(s) of , set the value equal to zero and solve.

Begin by recognizing that both sides of the equation have a root term of .

Using the power rule, we can set the exponents equal to each other.

Begin by recognizing that both sides of the equation have the same root term, .

We can use the power rule to combine exponents.

Set the exponents equal to each other.

is the only choice from those given that satisfies the equation. Substition of for gives:

Take the common logarithm of both sides and solve for :

, so can be rewritten as

One method: Take the natural logarithm of both sides and solve for :

Since , we can rewrite this equation by subsituting and applying the power rule:

This statement is identically false, which means that the original equation is identically false. There is no solution.

, so we can rewrite the equation as follows:

To find the x-intercepts, we set the numerator equal to zero and solve.

However, the square root of a number can be both positive and negative.

Therefore the roots will be

To find the y-intercepts, set and solve.

To find the x-intercepts, set the numerator equal to zero and solve.

We can simplify from here:

Now we need to rationalize. Because we have a square root on the bottom, we need to get rid of it. Since , we can multiply to get rid of the radical in the denominator.

Since we took a square root, remember that our answer can be either positive or negative, as a positive squared is positive and a negative squared is also positive.

To find the y-intercepts, set and solve.

To find the y-intercept, set and solve.

To find the x-intercepts, set the numerator equal to zero.

To find the y-intercept, set and solve.