2007-01-21 14:22:34 · 4 answers · asked by john m 1 in Science & Mathematics ➔ Mathematics
log 4 24 = x
4^x = 24
log both sides and bring the x to the front (Prop. of logs)
x log 4 = log 24 (Now the log has a base of 10, stand. on calc)
divide both sides by log 4
x = log 24/log 4
x = 2.29248125
2007-01-21 14:29:41 · answer #1 · answered by Anonymous · 2⤊ 0⤋
log[base 4](24)
The change of base formula is useful because most scientific calculators only deal with base 10 (which is the regular log button on the calculator) or base e (which is the ln button).
The change of base formula goes as follows:
log[base a](c) = log[base b](c) / log[base b](a)
For our case, we have
log[base 4](24)
And we want to change it to log base 10 or log base e. I'll choose log base 10, so we have
log[base 4](24) = log24 / log4
Use your calculator and you'll get an approximate value.
Similarly, you could also do ln(24) / ln(4) and get the same answer.
2007-01-21 14:30:16 · answer #2 · answered by Puggy 7 · 1⤊ 0⤋
By the change of base formula, it's 2.29248125... . Here's how it's done:
log_4 (24) = [log_10 (24)] / [log_10 (4)] =
1.380211242... / 0.602059991...] = 2.29248125...
CHECK: Evaluate 4^(2.29248125... ) on your calculator:
It's : 24 (!) So it checks out, correctly.
Live long and prosper.
2007-01-21 14:27:31 · answer #3 · answered by Dr Spock 6 · 0⤊ 0⤋
Just plug 4 and 24 into the formula and you get the answer. Type it into your calc and round off appropriately.
2007-01-21 14:26:53 · answer #4 · answered by hayharbr 7 · 0⤊ 0⤋
log4 24
= log(24) / log(4)
= 1.3802 / 0.6021
= 2.29
2007-01-21 14:33:27 · answer #5 · answered by Sheen 4 · 0⤊ 0⤋