Question

solve for x. 27^(2x)=9^(x-3)

Answer 1

i am not playing with logs this early

Answer 2

x = -3/2

Equalize the bases, and then solve for x.

Answer 3

thanks

Answer 4

No Problem.

Answer 5

\[27^{2x}=9^{x-3}\]\[3^{6x} = 3^{2x-6}\] then just set \[6x = 2x -3\] No logs necessary!

Answer 6

27^(2x)=9^(x-3)

Create equivalent expressions in the equation that all have equal bases.
3^(3(2x))=3^(2(x-3))

Since the bases are the same, then two expressions are only equal if the exponents are also equal.
3(2x)=2(x-3)

Multiply 2 by each term inside the parentheses.
3(2x)=(2x-6)

Remove the parentheses around the expression 2x-6.
3(2x)=2x-6

Multiply 3 by each term inside the parentheses.
6x=2x-6

Since 2x contains the variable to solve for, move it to the left-hand side of the equation by subtracting 2x from both sides.
6x-2x=-6

Since 6x and -2x are like terms, add -2x to 6x to get 4x.
4x=-6

Divide each term in the equation by 4.
(4x)/(4)=-(6)/(4)

Simplify the left-hand side of the equation by canceling the common terms.
x=-(6)/(4)

Simplify the right-hand side of the equation by simplifying each term.
x=-(3)/(2)

Answer 7

Great explanation!

Answer 8

thanks apupo 03