Evaluate log base 49 of 343

Problem

(log_49)(343)

Solution

1. Identify the base and the argument of the logarithm. The base is 49 and the argument is 343

2. Express both numbers as powers of a common base. Since 49=7 and 343=7 we can rewrite the expression using base 7

3. Apply the change of base formula, which states (log_b)(a)=(log_c)(a)/(log_c)(b)

4. Substitute the values into the formula using c=7

(log_49)(343)=(log_7)(343)/(log_7)(49)

5. Simplify the numerator and denominator by evaluating the logarithms.

(log_7)(7)=3

(log_7)(7)=2

6. Divide the results to find the final value.

3/2=1.5

Final Answer

(log_49)(343)=3/2

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