Answer:
a = 1/100000 = 10^-6 and B= -6.25x10^-6
Explanation:
first we take log on both sides of equation;
log ay = b log(√x -5) because log a^x = x log a
log a + log y = b log (√x -5) ; reminder: log ab = log a+log b
first we find a;
we can rewrite the above equation to be;
log y = b log (√x -5) - log a
think about at which value of x the log (√x -5) become zero. we know log 1 is zero so if we take x to be 36. we see than log (√36 - 5) = log (1) = 0.
so we get, log y = bx0 - log a; log y = -log a.
log (100000) = -log(1/100000)
so a = 1/100000. (notice log 100000 is 5 and log (1/100000) is -5; -(-5) is 5. so a is 1/100000
now we find b.
rearrange the above equation we get;
log (√x -5) = a/b log a + 1/b log y.
we know log(√x -5) is 8 when log y is zero from the graph.
so this becomes;
8 = a/b log a + 1/b x 0.
8 = a/b log a + 0
we know the value of a know. substitute.
8 = 0.00001/b log( 0.00001)
b = 0.00001/8 log(0.00001)
b = 0.00001/8 x -5 = -6.25 x 10^ -6