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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Solving Equations with Log Terms and Other Terms

Example

Solve: log5 (5x + 10) - 1 = log5 25.

 Solution log5 (5x + 10) - 1 = log5 25 Step 1 Rewrite the equation with the logs on one side and the constant term on the other side. To make the calculations easier, rewrite the equation so the constant term is positive. Add 1 to both sides. Subtract log525 from both sides. log5 (5x + 10)  = log5 25 + 1log5 (5x + 10)  - log5 25 = 1 Step 2 Combine the logs into a single log. Use the Log of a Quotient Property. Step 3 Convert the equation to exponential form and solve. Convert to exponential form.Factor numerator and denominator. Cancel the common factor of 5. Multiply both sides by the LCD, 5. Subtract 2 from both sides. 25 = x + 2 23 = x

So, the solution is x = 23.

Note:

Here is a check of the solution:

 IsIs Is Is Is Is log5 (5x + 10) - 1log5 (5 Â· 23 + 10) - 1 log5 (125) - 1 log5 (53) - 1 3 - 1 2 = log5 25 = log5 25 = log5 25 = log5 52 = 2 = 2 ?? ? ? ? ? Yes