Solve 2097=5954.3{(e)^x*(-0.00896)}

$$2097=5954.3 {(e)^{ x \times (-0.00896) }}$$

Solve for x

$$x=\frac{3125\ln(59543)-3125\ln(20970)}{28}\approx 116.473872288$$

Steps Using Definition of Logarithm

Divide both sides by 5954.3.

$$\frac{2097}{5954.3}=e^{x\left(-0.00896\right)}$$

Expand \frac{2097}{5954.3} by multiplying both numerator and the denominator by 10.

$$\frac{20970}{59543}=e^{x\left(-0.00896\right)}$$

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

$$e^{x\left(-0.00896\right)}=\frac{20970}{59543}$$

Use the rules of exponents and logarithms to solve the equation.

$$e^{-0.00896x}=\frac{20970}{59543}$$

Take the logarithm of both sides of the equation.

$$\log(e^{-0.00896x})=\log(\frac{20970}{59543})$$

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

$$-0.00896x\log(e)=\log(\frac{20970}{59543})$$

Divide both sides by \log(e).

$$-0.00896x=\frac{\log(\frac{20970}{59543})}{\log(e)}$$

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

$$-0.00896x=\log_{e}\left(\frac{20970}{59543}\right)$$

Divide both sides of the equation by -0.00896, which is the same as multiplying both sides by the reciprocal of the fraction.

$$x=\frac{\ln(\frac{20970}{59543})}{-0.00896}$$

Solve for x (complex solution)

$$x=-\frac{i\times 3125\pi n_{1}}{14}+\frac{3125\ln(59543)}{28}-\frac{3125\ln(20970)}{28}$$

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