Solve the equation. 3^{x^{2}-4}=27^{x}

ffortunyu

ffortunyu

Answered question

2021-11-19

Solve the equation.
3x24=27x

Answer & Explanation

Keith Dooley

Keith Dooley

Beginner2021-11-20Added 14 answers

Step 1: Given 
3x24=27x 
To solve:For x 
Step 2: Solution 
3x24=27x 
3x24=33x 
Since the bases are the same, the exponents must be equal.
x24=3x 
x23x4=0 
(x-4)(x+1)=0 
x-4=0, x+1=0 
x=-1,4

Poul1963

Poul1963

Beginner2021-11-21Added 15 answers

Calculation: 
The given exponential equation is 3x24=27x
Use above mention method and solve the equation 3x24=27x as follows. 
The formula can be changed to read as
3x24=27x 
3x24=3( {3})x 
3x24=33x 
Thus, the new equivalent equation becomes 3x24=33x
Since the bases of the aforementioned equation are equal, set the exponents on both sides to the same value and solve for x as shown below.
3x24=33x 
x24=3x 
x23x4=0 
x24x+x4=0 
Simplified futher as, 
x(x-4)x+1(x-4)=0 
(x-4)(x+1)=0 
x-4=0 or x+1=0 
x=4 or x=-1 
Thus, the solution set of the equation 3x24=27x is {-1,4}. 
In the equation, x=-1 and x=4 can be substituted to confirm the solutions that were found.3x24=27x
Substitute x=-1 into 3x24=27x
3x24=27x 
3-12-4=27-1 
33=271 
127=127 [True statement] 
Similarly, substitute x=4 into 3x24=27x
3(4)24=274 
3164=(33)4 
312=312 [True statement] 
As a result, the equation's solution set 3x24=27x is {-1,4}.

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