Question

Find all the real-number roots of the equation. Give an exact expression for the root and also a calculator approximation rounded to three decimal places. 10^2^x + 2(10^x) − 63 = 0

Answer 1

To clarify: \[10^{2x}+2(10^{x)}-63=0\]

Answer 2

the program that I am using didn't take that answer. Instead I guess it was looking for the answer to be \[\log _{10} (7)\]\[\approx.845\]

Answer 3

I was being stupid. Sorry:
let 10^x = y
Therefore:\[10^{2x} + 2*10^x - 63 = y^2 +2y - 63 = 0\] Now use the quadratic formula and get that y = 7 or y = -9
Since we can't have log of a negative number:
\[x = \log_{10}7 \]