Evaluate 5 log base 5 of 7

Problem

5*(log_5)(7)

Solution

1. Identify the logarithmic property for coefficients, which states that a*(log_b)(c)=(log_b)(ca)

2. Apply the property to move the coefficient 5 into the exponent of the argument.

5*(log_5)(7)=(log_5)(7)

3. Identify the inverse property of logarithms and exponents, which states that b(log_b)(x)=x

4. Note that the original expression is in the form b*(log_b)(x) but the task asks to evaluate the product 5⋅(log_5)(7)

5. Calculate the value of the argument 7

7=16807

6. Rewrite the expression using the calculated value.

5*(log_5)(7)=(log_5)(16807)

Final Answer

5*(log_5)(7)=(log_5)(16807)

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