Question

Which of the following is equivalent to the expression below? Log7 7+ log7 343

Answer 1

The equivalent expression is log base 7 of 2401, making choice (C) the correct answer.

To simplify the expression log base 7 of 7 plus log base 7 of 343, we can use logarithmic properties. The first term, log base 7 of 7, is equal to 1, as any logarithm to the base of its own number is 1. The second term, log base 7 of 343, can be simplified by recognizing that 343 is 7^3. Therefore, log base 7 of 343 is equivalent to 3.

Now, combining both terms, we have log base 7 of 7 plus log base 7 of 343 equals 1 plus 3, which is 4. So, the given expression is equivalent to 4.

Now, let's examine the answer choices:

A. log base 7 of 49: This is equivalent to 2 because 7^2 equals 49. Not the same as the simplified expression.

B. log base 7 of 350: This doesn't simplify to the given expression.

C. log base 7 of 2401: This is equivalent to 4 because 7^4 equals 2401. It matches the simplified expression.

D. log 2401: The base is missing, making it ambiguous.

Therefore, the correct answer is (C) log base 7 of 2401, which is equivalent to the given expression log base 7 of 7 plus log base 7 of 343.

Answer 2

The first step is to remember the properties of logarithms

One of them are the addtive property:

When two logarithms have the same base and they are summing between them, their arguments can be multiplied.

`\log_a(x)+\log_a(y)=\log_a(x*y)`

Now solve your problem:

`\log_77+\log_7343=\log_7(7*343)=\log_7(2401)`