Solve 1700=850{left(1+0.092/12right)}^x

$$1700 = 850 { \left(1+ \frac{ 0.092 }{ 12 } \right) }^{ x }$$

Solve for x

$$x=\log_{\frac{3023}{3000}}\left(2\right)\approx 90.756634248$$

Steps Using Definition of Logarithm

Divide both sides by 850.

$$\frac{1700}{850}=\left(1+\frac{0.092}{12}\right)^{x}$$

Divide 1700 by 850 to get 2.

$$2=\left(1+\frac{0.092}{12}\right)^{x}$$

Expand \frac{0.092}{12} by multiplying both numerator and the denominator by 1000.

$$2=\left(1+\frac{92}{12000}\right)^{x}$$

Reduce the fraction \frac{92}{12000} to lowest terms by extracting and canceling out 4.

$$2=\left(1+\frac{23}{3000}\right)^{x}$$

Add 1 and \frac{23}{3000} to get \frac{3023}{3000}.

$$2=\left(\frac{3023}{3000}\right)^{x}$$

Swap sides so that all variable terms are on the left hand side.

$$\left(\frac{3023}{3000}\right)^{x}=2$$

Take the logarithm of both sides of the equation.

$$\log(\left(\frac{3023}{3000}\right)^{x})=\log(2)$$

The logarithm of a number raised to a power is the power times the logarithm of the number.

$$x\log(\frac{3023}{3000})=\log(2)$$

Divide both sides by \log(\frac{3023}{3000}).

$$x=\frac{\log(2)}{\log(\frac{3023}{3000})}$$

By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$x=\log_{\frac{3023}{3000}}\left(2\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(\frac{3023}{3000})}+\log_{\frac{3023}{3000}}\left(2\right)$$

$$n_{1}\in \mathrm{Z}$$