2007-03-03 15:07:01 · 5 answers · asked by arbpdx1 1 in Science & Mathematics ➔ Mathematics
Let x = log[base 5](390625)
Then
5^x = 390625
5^x = 25 * 15625
5^x = 25 * 25 * 625
5^x = 25 * 25 * 25 * 25
But, 25 = 5^2, so
5^x = (5^2)(5^2)(5^2)(5^2)
And whenever we two numbers with the same base but different exponents, we can add the exponents.
5^x = 5^(2 + 2 + 2 + 2)
5^x = 5^8
Therefore, equating the powers,
x = 8
2007-03-03 15:11:09 · answer #1 · answered by Puggy 7 · 0⤊ 0⤋
5^x=390625
x log5 = log390625
[Divide both sides by log 5]
x=8
Therefore the expression log[base 5](390625) equals 8
2007-03-03 15:51:33 · answer #2 · answered by abcde12345 4 · 0⤊ 0⤋
The easiest way to do these is to use the change of base formula. Natural logarithm(390625)/natural logarithm(5).
12.8755033/1.609437912=8
The natural logarith is the LN key on your calculator. The common log is base ten; it is usually marked LOG on your calculator. Common can be used just as easily the natural log.
2007-03-03 15:27:20 · answer #3 · answered by n9qs 3 · 0⤊ 0⤋
means 5^x=390625
x=8
2007-03-03 15:09:51 · answer #4 · answered by leo 6 · 1⤊ 0⤋
log(base5)(390625)
=[log (base10) (390625) / log(base10) (5)]
=5.591/0.6989=8.0
2007-03-03 15:27:04 · answer #5 · answered by llcold 2 · 0⤊ 0⤋