If points (0.4, 25) and (1.2, 53) lie on the graph of
log y = B + a log x solve for a.
A) $a$ = 0.684
B) $a$ = 0.916
C) $a$ = 1.182
D) $a$ = 1.544

Question

If points (0.4, 25) and (1.2, 53) lie on the graph of 
log y = B + a log x solve for a.
A) $a$ = 0.684
B) $a$ = 0.916
C) $a$ = 1.182
D) $a$ = 1.544

Quizplus · Accepted Answer

We start by using the properties of logarithms to rewrite the equation as:

log y = B + a log x
log y = log x^a + B
y = 10^(log x^a + B)
y = 10^(B) * 10^(log x^a)
y = K x^a, where K = 10^(B)

We can now use the two given points to form a system of equations:

25 = K (0.4)^a
53 = K (1.2)^a

Dividing the second equation by the first gives:

53/25 = (1.2/0.4)^a
a = log (53/25) / log (1.2/0.4) ≈ 0.684

Therefore, the answer is choice A.

If Points (0 aaa = 0684 B) aaa = 0916 C) aaa = 1182 D)