Question

Which graph represents the equation

Answer 1

Answer:

First graph

Step-by-step explanation:

To identify which graph represents the equation, we can find an x-intercept of a function by substituting y = 0 in.

That will result with $\displaystyle{0 = \log_3 x + 1}$. Then we solve the equation for x:

$\displaystyle{-1 = \log_3 x}$

Apply logarithm conversion to exponential:

$\displaystyle{\log_a b = n \to a^n = b}$

Therefore:

$\displaystyle{\log_3 x = -1 \to 3^{-1} = x}$

Apply law of exponent for negative exponent to simplify:

$\displaystyle{a^{-n} = \dfrac{1}{a^n}}$

Therefore:

$\displaystyle{x = 3^{-1}}\\\\\displaystyle{x = \dfrac{1}{3}}$

Since the logarithm has positive integer base then we can cut off choice 2 and choice 3 since that only applies to negative logarithm and fraction base of logarithm.

The only choices we have are first and fourth but fourth graph has x-intercept equal to 3. However, we solve for x-intercept and receive 1/3 as our x-intercept which is between 0 and 1.

Henceforth, the first graph represents the equation.