Evaluate without using logarithm tables (a) 2log5 + log36 - log9

Question

ScanSolve AI Tutor · Accepted Answer

Here's how to evaluate the expression using logarithm properties:

Apply the power rule of logarithms, $a \log b = \log (b^a)$ , to the first term.
$2\log5 = \log(5^2) = \log25$
Substitute this back into the original expression.
$\log25 + \log36 - \log9$
Apply the product rule of logarithms, $\log a + \log b = \log (a \times b)$ , to the first two terms.
$\log25 + \log36 = \log(25 \times 36) = \log900$
Substitute this back into the expression.
$\log900 - \log9$
Apply the quotient rule of logarithms, $\log a - \log b = \log \left(\frac{a}{b}\right)$ .
$\log900 - \log9 = \log\left(\frac{900}{9}\right) = \log100$
Evaluate $\log100$ .
Since no base is specified, it is assumed to be base 10.
$\log_{10}100 = 2 \quad \text{because} \quad 10^2 = 100$
The final answer is 2.

Answer