Solve the equation. 27^{x-1}=9^{2x-3}

Ramsey

Ramsey

Answered question

2021-09-27

Solve the equation.
27x1=92x3

Answer & Explanation

Khribechy

Khribechy

Skilled2021-09-28Added 100 answers

Step 1
To solve the exponential equation: 27x1=92x3.
Solution:
27x1=92x3
On simplifying further we get:
(27)x1=(9)2x3(33)x1=(32)2x3 (using, 27=33,9=32)
33(x1)=32(2x3) (using, (am)n=amn)
Now as base (3) is equal on both sides of the equation,we can equate the powers.
3(x1)=2(2x3)
3x3=4x6
3x4x=6+3
x=3
x=3
Step 2
Result:
Required solution is: x=3.

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