If 3^{2x - 1} = 27, what is the value of x? — SAT

If $3^{2x - 1} = 27$ , what is the value of $x$ ?

To solve the equation

3^{2x - 1} = 27

, we first express 27 as a power of 3, which is

3^3

. Since the bases are the same, we set the exponents equal to each other to get

2x - 1 = 3

. Adding 1 to both sides gives

2x = 4

, and dividing both sides by 2 gives the value of

x

as 2.

Express 27 with a base of 3

3^{2x - 1} = 3^3

To solve an exponential equation, we need to write both sides of the equation with a common base.

Set the exponents equal to each other

2x - 1 = 3

Since the bases are equal, their exponents must also be equal.

Solve the linear equation for

x

x = 2

Add 1 to both sides to get

2x = 4

, and then divide both sides by 2 to isolate

x

Solving exponential equations by finding a common base

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