Question

Rogelio argues that log5 15635 is between 6 and 7 because 6^5 =7776 and 7^5=16807. Explain why you agree or disagree

Answer 1

Expressions can be represented as logarithms and exponents

Rogelio argument is correct

How to determine if Rogelio's claim is true

The logarithmic equation is given as:

$\log_5(15635)$

Apply logarithm rule, to rewrite the logarithmic equation

$\log_5(15635) = \frac{\log(15635)}{\log(5)}$

Evaluate the individual logarithmic expressions

$\log_5(15635) = \frac{4.1941}{0.6990}$

Evaluate the quotient (i.e. divide the expression)

$\log_5(15635) = 6.0001$

The above equation shows that $\log_5(15635)$ is between 6 and 7

Hence, Rogelio argument is correct

Read more about equivalent expressions at:

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