If \log_3(2x - 1) = 2, what is the value of x? — ACT

If $\log_3(2x - 1) = 2$ , what is the value of $x$ ?

Answer: 5

The value of

x

5

Converting the logarithmic equation

\log_3(2x - 1) = 2

to its equivalent exponential form yields

3^2 = 2x - 1

. Simplifying the exponent gives

9 = 2x - 1

. Adding

1

to both sides results in

10 = 2x

, and dividing by

2

gives

x = 5

Rewrite the logarithmic equation in exponential form.

2x - 1 = 3^2

By definition,

\log_b(y) = z

is equivalent to

b^z = y

Evaluate the exponent

3^2

2x - 1 = 9

Calculating

3

squared yields

9

Solve the linear equation for

x

2x = 10

, which simplifies to

x = 5

Adding

1

to both sides and then dividing by

2

isolates

x

Converting logarithmic equations to exponential equations

Estimated Time:45s

Question