If \log_3(x + 4) = 4, what is the value of x? — ACT

If $\log_3(x + 4) = 4$ , what is the value of $x$ ?

Answer: 77

The value of

x

is 77.

The correct answer is 77. To solve the equation

\log_3(x + 4) = 4

, convert the equation from its logarithmic form to its exponential form. Since

\log_b(a) = c

means

b^c = a

, the equation becomes

3^4 = x + 4

. Calculating

3^4

yields 81. Thus,

81 = x + 4

. Subtracting 4 from both sides gives

x = 77

Rewrite the logarithmic equation in exponential form.

x + 4 = 3^4

By definition,

\log_b(a) = c

is equivalent to

b^c = a

Calculate the value of the exponential expression.

3^4 = 81

3^4 = 3 \times 3 \times 3 \times 3 = 81

Solve for

x

by isolating the variable.

x = 77

Subtract 4 from both sides of the equation:

81 - 4 = 77

Converting logarithmic equations to exponential form

Question