Question

Which statement is true for log Subscript 3 Baseline (x + 1) = 2

Answer 1

Option A: $x+1=3^{2}$ is the correct statement

Explanation:

The expression is $\log _{3}(x+1)=2$

We need to determine the statement which is true for the expression $\log _{3}(x+1)=2$

Using logarithmic definition, if $\log _{a}(b)=c$ then $b=a^{c}$, we have,

$x+1=3^{2}$

Simplifying,

$x+1=9$

     $x=8$

Now, we shall determine the statement which is true for the expression $\log _{3}(x+1)=2$

Option A: $x+1=3^{2}$

Simplifying, we get,

$x+1=9$

     $x=8$

Thus, the expression $x+1=3^{2}$ is equivalent to $\log _{3}(x+1)=2$

Hence, Option A is the correct answer.

Option B: $x+1=2^3$

Simplifying, we get,

$x+1=8$

     $x=7$

Since, the values of x from both the expressions are not equal.

Then, the expression  $x+1=2^3$ is not equivalent to $\log _{3}(x+1)=2$

Hence, Option B is not the correct answer.

Option C: $2(x+1)=3$

Simplifying, we get,

$2x+2=3$

      $2x=1$

       $x=\frac{1}{2}$

Since, the values of x from both the expressions are not equal.

Then, the expression  $2(x+1)=3$ is not equivalent to $\log _{3}(x+1)=2$

Hence, Option C is not the correct answer.

Option D: $3(x+1)=2$

Simplifying, we get,

$3x+3=2$

      $3x=-1$

       $x=-\frac{1}{3}$

Since, the values of x from both the expressions are not equal.

Then, the expression  $3(x+1)=2$ is not equivalent to $\log _{3}(x+1)=2$

Hence, Option D is not the correct answer.

Answer 2

Answer:

Option A

Step-by-step explanation:

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