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For the following exercises, solve the equation for x, if there is a solution. Then graph both sides of the equation, and observe the point of intersection (if it exists) to verify the solution. log3 (x) + 3 = 2

For the following exercises, solve the equation for x, if there is a solution. Then graph both sides of the equation, and observe the point of intersection (if it exists) to verify the solution.

log3 (x) + 3 = 2

Expert Solution

Consider the following equation;

log3(x) + 3 = 2

Add -3 to both the sides of the equation as follows:

log3(x) + 3 – 3 = 2 – 3

log3(x) = -1

Use the logarithmic property a = logb(ba) as follows:

log3(x) = log3(3-1)

Use the following logarithmic property

logb{f(x)} = logb{g(x)}

⇒ f(x) = g(x)

Therefore,

x = 1/3

Therefore, the value of ‘x’ is 1/3.

Use maple to plot the graph both sides of the equation as shown below:

From the graph above, the two graphs intersect at x = 1/3.

Therefore, the value of ‘x’ is 1/3.

Nabeel answered 1 year ago

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