How do you solve this equation for the variable? 3^2m= 81

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violy's profile pic

violy | High School Teacher | (Level 1) Associate Educator

Posted on

We can first rewrite 81 as an exponential with base 3. 

We know that 3*3*3*3 = 81. So, 81 = 3^4.

We will have:

3^2m = 3^4

Using natrual logarithm on both sides. 

ln3^2m = ln3^4

Use the property: lna^b = blna.

2mln3 = 4ln3

Divide both sides by ln3. 

2m = 4

Divide both sides by 2. 

m = 2

pramodpandey's profile pic

pramodpandey | College Teacher | (Level 3) Valedictorian

Posted on

3^2m= 81




Factor above expression by `A^2-B^2=(A-B)(A+B)`



`because 3^m+9!=0AA m`



oldnick's profile pic

oldnick | (Level 1) Valedictorian

Posted on




using natural log:

`2m ln3= 4ln 3`



rosey-girl's profile pic

rosey-girl | Student, Grade 12 | (Level 1) Valedictorian

Posted on

this is not how you do it, sorry but my teacher told me to use natural log or log base.

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