SOLUTION: Write y as a function of x. log10 y= -.75logx - 1.76 I am not sure if this is right, but I have tried to write the correct function, log10 y= -.75logx - 1.76 y= 10^-.75

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Write y as a function of x. log10 y= -.75logx - 1.76 I am not sure if this is right, but I have tried to write the correct function, log10 y= -.75logx - 1.76 y= 10^-.75      Log On


   



Question 718213: Write y as a function of x.
log10 y= -.75logx - 1.76
I am not sure if this is right, but I have tried to write the correct function,
log10 y= -.75logx - 1.76
y= 10^-.75logx-1.76
or
y= 10^-.75x * 10^-1.76
Please explain which one is right, if any, and why. Thanks!

Found 2 solutions by jsmallt9, josmiceli:
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
log%2810%2C+%28y%29%29=+-.75logx+-+1.76
To solve for y, all we have to do is rewrite the equation in exponential form. In general, log%28a%2C+%28p%29%29+=+q is equivalent to p+=+a%5Eq. In words, this pattern tells us that the argument of the log, p, is equal to the base of the log, a, with an exponent of the whole right-hand side of the logarithmic equation.

Using this pattern, our log's argument, y, is equal to the base of our log, 10, with an exponent of the entire right-hand side:
y+=+10%5E%28-.75logx+-+1.76%29
which makes
y= 10^-.75logx-1.76
almost right. You just need parentheses on the exponent:
y= 10^(-.75logx-1.76)

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The way I see it,
+y=+10%5E%28+-.75%2Alog%28x%29+-+1.76+%29+
+y+=+1+%2F+10%5E%28+.75%2Alog%28x%29+%2B+1.76+%29+
+y+=+%281+%2F+10%5E%28.75%2Alog%28x%29+%29+%29+%2A+%28+1+%2F+10%5E1.76+%29+
+y+=+%28+1+%2F+10%5E%28+log%28+x%5E.75%29%29+%29+%2A+%28+1+%2F+10%5E1.76+%29+
+y+=+%28+1+%2F+x%5E.75+%29%2A%28+1+%2F+%2810%5E1.76%29+%29+
+y+=+1%2F%28+10%5E1.76%2A%28x%5E.75%29%29+
------------------------
I'll try to check this by saying +x+=+10%5E4+
+y+=+1%2F%28+10%5E1.76%2A%2810%5E4%29%5E.75+%29+
+y+=+1%2F%28+10%5E1.76%2A10%5E3+%29+
+y+=+1%2F%28+10%5E4.76+%29+
+y+=+1+%2F+57543.994%0D%0A%7B%7B%7B+y+=+.000017378+
and
+y=+10%5E%28+-.75%2Alog%28x%29+-+1.76+%29+
+y=+10%5E%28+-.75%2Alog%2810%5E4%29+-+1.76+%29+
+y+=+10%5E%28+-.75%2A4+-+1.76+%29+
+y+=+10%5E%28+-4.76+%29+
+y+=+000017378+
This seems to check