Tutorial Exercise Evaluate the logarithm at the given value of x without using a calculator. Function Value f(x)=log_(25)(x),x=5 Step 1 Substitute 5 for x in the function. Step 2 Notice that sqrt(25)=5. Rewrite without the square root symbol. 25^((1)/(2)) sqrt(2)=5 Step 3 Recall the Power Property of logarithms which states that if a is a posi

Question

Tutorial Exercise Evaluate the logarithm at the given value of

x

without using a calculator.

 Function  Value 
f(x)=log_(25)(x),x=5

Step 1 Substitute 5 for

x

in the function. Step 2 Notice that

\sqrt(25)=5

. Rewrite without the square root symbol.

25^((1)/(2))\sqrt(2)=5

Step 3 Recall the Power Property of logarithms which states that if

a

is a positive number and

n

is a real number such that

a!=1

and if

u

is a positive real number, then

log_(a)(u^(n))=nlog_(a)(u)

Use this property to simplify the expression.

log_(25)(25^((1)/(2)))=log_(25)(25)

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