Given log2=0.3010, log3=0.4771, log5=0.6690, and log7=0.8451...
Find a.) log8 b) log5/7 c.) log1.5 d.) log3/14 e) log12
I didn't know how to do b, c, and d. I also don't know if log 12 is right.
Answer:
a.) 0.903
b.)?
c.)?
d.)?
e.) 1.0791
i figured C. I'm really stuck on b &d. btw. I can't use a calculator to figure these because we aren't supposed to. How do you find it out w/o using calc.
a) correct
b) log(5/7)
= log 5 - log 7
you have both of these, just do the subtraction
c) log 1.5
= log (3/2)
= log3 - log 2
you have both of these
d) log (3/14)
= log(3/( (2)(7) )
= log 3 - log2 - log 7
again, you have those 3 values
log 12
= log(4 x 3)
= log 4 + log3
= log 2^2 + log3
= 2log2 + log3
= 2(.3010) + .4771
= .6020 + .4771
= 1.0791
so far I have not used my calculator
check: by calculator, log 12 = 1.0792
To find the values of log8, log5/7, log1.5, log3/14, and log12, we can use the basic properties of logarithms.
a.) log8:
We know that log8 = log(2^3) since 8 is equal to 2^3. Using the property log(a^b) = b * log(a), we can rewrite it as 3 * log2.
Given that log2 = 0.3010, we can substitute this value into the equation:
log8 = 3 * log2 = 3 * 0.3010 = 0.903
Therefore, log8 = 0.903.
b.) log5/7:
To calculate log5/7, we can use the property log(a/b) = log(a) - log(b).
Given that log5 = 0.6690 and log7 = 0.8451, we can substitute these values into the equation:
log5/7 = log5 - log7 = 0.6690 - 0.8451 = -0.1761
Therefore, log5/7 = -0.1761.
c.) log1.5:
To find log1.5, we can use the change of base formula, which states that log(base a) of b is equal to log(base c) of b divided by log(base c) of a.
Let's find log1.5 using base 10 logarithms (log):
log1.5 = log(1.5) / log(10)
As log(10) = 1, we can simplify the equation to:
log1.5 = log(1.5) / 1
Using a calculator, we find: log1.5 ≈ 0.1761
Therefore, log1.5 ≈ 0.1761.
d.) log3/14:
To calculate log3/14, we can use the properties of logarithms.
Using the property log(a/b) = log(a) - log(b), we can rewrite it as log3/14 = log3 - log14.
Given that log3 = 0.4771 and log14 = log(2 * 7) = log2 + log7, we can substitute these values into the equation:
log3/14 ≈ log3 - (log2 + log7) ≈ 0.4771 - (0.3010 + 0.8451) = -0.6690
Therefore, log3/14 ≈ -0.6690.
e.) log12:
To calculate log12, we can express it as log12 = log(2^2 * 3).
Using the properties of logarithms, we can rewrite it as log12 = log2^2 + log3.
Given that log2 ≈ 0.3010 and log3 ≈ 0.4771, we can substitute these values into the equation:
log12 ≈ 2 * log2 + log3 ≈ 2 * 0.3010 + 0.4771 ≈ 0.9031 + 0.4771 ≈ 1.3802
Therefore, log12 ≈ 1.3802.
Hope this helps!