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.