If loga 8=2.079, loga 5=1.609, and loga 3=1.099, find the following?
19.) loga 8/3 is this 1.89?
20.) loga 24 Not sure
21.) loga 25 not sure how to do this
make use of your main "log rules"
log (8/3) = log 8 - log 3 = 2.079 - 1.099
= 0.98
log 24 = log (3x8) = log 3 + log 8
= ....
log 25 = log 5^2
= 2 log 5
= ...
Okay I got it
log (8/3) = log 8 - log 3 = 2.079 - 1.099
= 0.98
log 24 = log (3x8) = log 3 + log 8
= 3.688
log 25 = log 5^2
= 2 log 5
= 2.138
great,
BTW, how would you find 'a' itself?
To find the values of the given logarithmic expressions, we can use the properties of logarithms.
19.) To find loga 8/3:
We can use the property loga (x/y) = loga x - loga y.
Therefore, we have:
loga 8/3 = loga 8 - loga 3 = 2.079 - 1.099 = 0.980
So, loga 8/3 is approximately 0.980, not 1.89.
20.) To find loga 24:
We can use the property loga (x*y) = loga x + loga y.
Therefore, we can write loga 24 as loga (8 * 3) = loga 8 + loga 3.
We already know that loga 8 = 2.079 and loga 3 = 1.099, so we can substitute these values:
loga 24 = 2.079 + 1.099 = 3.178
So, loga 24 is approximately 3.178.
21.) To find loga 25:
We can use the property loga (x^y) = y * loga x.
Therefore, we can write loga 25 as 2 * loga 5.
We already know that loga 5 = 1.609, so we can substitute this value:
loga 25 = 2 * 1.609 = 3.218
So, loga 25 is approximately 3.218.