Question

Calculate this logarithmic expression

Answer 1

The solution of the logarithmic expression $\log_2(17 -\sqrt{19}) + \log_2(17 +\sqrt{19})$ is $\log_2[270]$

How to solve the logarithmic expression?

The expression is given as:

$\log_2(17 -\sqrt{19}) + \log_2(17 +\sqrt{19})$

Apply the product law of logarithm

$\log_2[(17 -\sqrt{19}) *(17 +\sqrt{19})]$

Apply the difference of two squares

$\log_2[(17^2 -(\sqrt{19})^2]$

Evaluate the squares

$\log_2[(289 -19]$

Evaluate the difference

$\log_2[270]$

Hence, the solution of the logarithmic expression $\log_2(17 -\sqrt{19}) + \log_2(17 +\sqrt{19})$ is $\log_2[270]$

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