log(2.848) = 1.602 * 1.778
Is this a true statement? Why or why not?
log(2.848)=
log(2*sqrt2)=log2+logsqrt2
= log2+1/2 log2=3/2 log2 which is nowhere near 1.602*1.778
additionally, the product on the right is approximately 2.4
taking the antilog of each side
antilog 2.848 is between zero and one (2.8 is less than ten).
the right side is 2.4
so it icannot be true.
Thank you for the clarification!
To determine whether the statement "log(2.848) = 1.602 * 1.778" is true or not, we need to evaluate both sides of the equation separately.
Let's start with the left side of the equation:
log(2.848)
To find the value of this logarithm, we need to know the base. The most common base used for logarithms is base 10 (logarithm base 10, or simply log). However, we can also use other bases like natural logarithm (base e) or any other specified base.
Assuming that the base is not specified, we will assume it to be base 10. So, log(2.848) represents the logarithm of 2.848 to the base 10.
Using a calculator, we find that log(2.848) is approximately 0.4542.
Now, let's evaluate the right side of the equation:
1.602 * 1.778
Multiplying these two numbers, we get approximately 2.8496.
Comparing the values:
0.4542 (left side) vs. 2.8496 (right side)
Since the left side (0.4542) is not equal to the right side (2.8496), the statement "log(2.848) = 1.602 * 1.778" is NOT true.
In conclusion, the given statement is false because the left side and the right side of the equation do not have the same value when evaluated.