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DaniilM [7]
2 years ago
14

Which of the following is true regarding the solution to the logarithmic equation below? log Subscript 2 Baseline (x + 11) = 4.

x + 11 = 2 Superscript 4. x + 11 = 16. x = 5. x = 5 is not a true solution because log Subscript 5 Baseline (16) not-equals 2 x = 5 is not a true solution because log Subscript 5 Baseline (16) not-equals 4 x = 5 is a true solution because log Subscript 2 Baseline (16) = 4 x = 5 is a true solution because log Subscript 4 Baseline (16) = 2
Mathematics
1 answer:
meriva2 years ago
5 0

Answer:

Option C.

Step-by-step explanation:

The given logarithmic equation is

\log_2(x+11)=4

It can be written as

(x+11)=2^4     [\because log_ax=y\Leftrightarrow x=a^y]

x+11=16

x=5

Now, to check whether x=5 is a true solution or not. Substitute x=5 in the LHS of given equation.

LHS=\log_2(5+11)

LHS=\log_2(16)

LHS=\log_22^4

LHS=4     [\because log_aa^x=x]

LHS=RHS

Hence, x=5 is a true solution because \log_2(16)=4.

Therefore, the correct option is C.

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