log_3(x+1)^2=2  I have no clue on hoe to solve this...

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electreto05 | College Teacher | (Level 1) Assistant Educator

Posted on

The logarithm of a number is the value that should raise the base to obtain this number. For example, the logarithm of the unit, with a base 10, is zero because the number 10 to the zero power is equal to unity.

With this in mind and considering that our base is 3, we take the above expression and pose:

Log_3(x + 1)^2 = 2

3^2 = (x + 1)^2

Taking the square root of both sides:

x + 1 = 3

x = 3 – 1 

x = 2

Based on the initial explanation we make a verification. The base of the logarithm is 3, then we have:

3^2 = (x + 1)^2

9 = (2 + 1)^2

9 = 9

So that the value of x in our equation is x = 2

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embizze | High School Teacher | (Level 1) Educator Emeritus

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When you take the square root, you will get two answers. In this case, -4 is another solution.

The graph:

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neeldod | Student, Grade 11 | (Level 1) Honors

Posted on

Log3(x+1)2=2

You use the law of log that is a power will be brought down to make the log look as follows:

2Log3(x+1)=2

Then you divide both sides by 2

Log3(x+1)=1

3=x+1

3-1=x

2=x

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

This method gives one of the solutions but loses the other. After bringing the power out front and dividing you should have:

`log_3|x+1|=1 ` so |x+1|=3 and you get both answers.

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