write y as a power function of x
log y = .76 log x - 2.4
can you show me the step by step? my main problem is getting the log on one side to teh other and writing as a single log please help huge test tmrw!
2006-10-09 13:41:32 · 2 answers · asked by abbs 2 in Science & Mathematics ➔ Mathematics
I'll assume that by "log y" you mean the common logarithm of y (base 10), as opposed to the natural logarithm (base e), which is written as ln y.
Use the property b log x = log x^b:
log y = log x^(.76) - 2.4
Exponentiate both sides:
10^(log y) = 10^(log x^(.76) - 2.4)
Use property 10^(log a) = a:
y = 10^(log x^(.76) - 2.4)
Use property a^(x-y) = a^x / a^y:
y = 10^(log x^(.76)) / 10^(2.4)
Use 10^(log a) = a:
y = x^(.76) / 10^(2.4)
2006-10-09 13:51:37 · answer #1 · answered by James L 5 · 1⤊ 0⤋
log y = log x^.76 - 2.4
log y - log x^.76 = -2.4
log (y/(x^.76) = -2.4
y/(x^.76) = 10 ^ (-2.4)
y = 10^(-2.4) x^.76
To be perfectly simplified, we shouldn't have negative exponents, so move it to the denominator:
y = x^.76 / (10^2.4)
2006-10-09 21:06:05 · answer #2 · answered by Anonymous · 0⤊ 0⤋