Question

Evaluate log 1 + tan square 45 whole square base 4

Answer 1

Answer:

1

Step-by-step explanation:

$log_{ {4 } }(1 + \ {tan}^{2} (45))^{2}$

$log_{4 } ({1 + 1})^{2}$

$log_{4}({2}^{2})$

$log_{4}(4)$

$= 1$

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Answer 2

$\displaystyle \sf{ log_{4}{(1 + {tan}^{2} \: {45}^{ \circ} )}^{2} } = \bf \: 1$

Given :

$\displaystyle \sf{ log_{4}{(1 + {tan}^{2} \: {45}^{ \circ} )}^{2} }$

To find :

The value of the expression

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

$\displaystyle \sf{ log_{4}{(1 + {tan}^{2} \: {45}^{ \circ} )}^{2} }$

Step 2 of 2 :

Find the value of the expression

$\displaystyle \sf{ log_{4}{(1 + {tan}^{2} \: {45}^{ \circ} )}^{2} }$

$\displaystyle \sf{ = log_{4}{(1 +1 )}^{2} }$

$\displaystyle \sf{= log_{4}{(2 )}^{2} }$

$\displaystyle \sf{ = log_{4}(4) }$

$\displaystyle \sf{ = 1 \: \: \: \bigg[ \: \because \:log_{a}(a) = 1 \bigg] }$

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