Logarithmic and Exponential Equations Score: 5.5/10 Answered: 7/10 Solve and Check: log_(3)(x)+log_(3)(x+8)=2 If there is a solution, enter as an integer or reduced fraction If there are multiple solutions, separate them using commas. For no solutions, click No solution. One or more solutions: square No solution

Question

Logarithmic and Exponential Equations Score: 5.5/10 Answered: 7/10 Solve and Check: log_(3)(x)+log_(3)(x+8)=2 If there is a solution, enter as an integer or reduced fraction If there are multiple solutions, separate them using commas. For no solutions, click No solution. One or more solutions: square No solution

Answer 1

To solve the equation

, we can use the properties of logarithms to combine the two logarithmic terms on the left side of the equation.Using the product rule of logarithms, we have:

So the equation becomes:

Now, we can use the definition of a logarithm to rewrite the equation in exponential form:

Simplifying the equation, we get:

Rearranging the terms, we have:

This is a quadratic equation, which can be solved using the quadratic formula:

In this case,

,

, and

. Plugging these values into the quadratic formula, we get:

So the solutions are:

Therefore, the solutions to the equation

are

and

.

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