Algebra Tutorials!

 Saturday 13th of July

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 Depdendent Variable

 Number of equations to solve: 23456789
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 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
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 Solve for:

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Solving Equations with One Log Term

In the next three examples, the variable x represents the base of the logarithm. Remember, the base of a logarithm must be positive but not 1.

Example 1

Solve: logx 100 = 2.

 Solution Rewrite in exponential form. Take the square root of each side. Simplify. logx100 = x2 =  x =  x = 2100 Â± 10

Since x is the base, it must be positive. Therefore, -10 is not a solution. The solution is x = +10.

So, log10100 = 2. The solution checks since 102 = 100. You may also check the solution on a calculator.

Example 2

Solve:

 Solution logx 8 Rewrite in exponential form. Rewrite using a radical. Square both sides. x1/2 x = 8= 8 = 64

So,

Note:

The solution of is x = 64.

Here is a check.

Example 3

Solve:

 Solution Rewrite in exponential form. Rewrite x-2 as . Cross multiply. Take the square root of each side. Simplify. x2 = 16x = Â± x = Â± 4
Since x is the base, it must be positive. Therefore, -4 is not a solution. The solution is x = + 4.

So, We leave the check to you.