Can we solve this equation without choices ?

9^x-8^x=3

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- Apr 12th 2012, 10:33 AMMhmh96equation
Can we solve this equation without choices ?

9^x-8^x=3 - Apr 12th 2012, 09:40 PMprincepsRe: equation
Yes , graphically....

- Apr 12th 2012, 10:40 PMa tutorRe: equation
or use an iterative method, for example...

$\displaystyle x_{n+1}=x_n-\frac{9^{x_n}-8^{x_n}-3}{9^{x_n}\ln 9 -8^{x_n} \ln 8}$

Starting with $\displaystyle x_o=1$

$\displaystyle x_5=1.367251988$

$\displaystyle x_6=1.367251981$

The above uses Newton's method.