Evaluate the expression without using a calculator:
log4(2)= ____?
Use a calculator to find the logarithm accurate to four decimal places:
log4(27)= ____?
log4(2)= ____?
What exponent must 4 be raised to, to obtain 2
that is,
4^? = 2
Isn't √4 = 2 ? or
4^(1/2) = 2
for the second,
log4 27
= log 27/log 4 , now use your calculator.
To evaluate the expression log4(2) without using a calculator, we need to understand what the logarithm means.
In this case, log4(2) means "To what power must 4 be raised to obtain 2?" Logarithms are the inverse function of exponentiation.
Let's start by simplifying log4(2) using the change of base formula:
log4(2) = log(2) / log(4)
We can use the natural logarithm for the numerator (log(2)) and the common logarithm for the denominator (log(4)).
Using ln(2) ≈ 0.6931 and log(4) ≈ 0.6021, we can calculate:
log4(2) ≈ 0.6931 / 0.6021 ≈ 1.1513
Therefore, without using a calculator, log4(2) is approximately equal to 1.1513.
Now, to evaluate log4(27) accurately to four decimal places, we can use a calculator:
log4(27) ≈ 1.7923
Therefore, using a calculator, log4(27) is approximately equal to 1.7923.