Solve 1=2,5^n(frac{-2.68{10,85x})}

$$1 = 2,5 ^ { n ( \frac { - 2.68 } { 10,85 x } ) }$$

Solve for n

$$n=0$$

Steps Using Definition of Logarithm

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

$$2.5^{n\times \frac{-2.68}{10.85x}}=1$$

Reorder the terms.

$$2.5^{\left(-\frac{2.68}{10.85x}\right)n}=1$$

Reorder the terms.

$$2.5^{-\frac{2.68}{10.85x}n}=1$$

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

$$2.5^{\left(-\frac{268}{1085x}\right)n}=1$$

Take the logarithm of both sides of the equation.

$$\log(2.5^{\left(-\frac{268}{1085x}\right)n})=\log(1)$$

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

$$\left(-\frac{268}{1085x}\right)n\log(2.5)=\log(1)$$

Divide both sides by \log(2.5).

$$\left(-\frac{268}{1085x}\right)n=\frac{\log(1)}{\log(2.5)}$$

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

$$\left(-\frac{268}{1085x}\right)n=\log_{2.5}\left(1\right)$$

Divide both sides by -\frac{268}{1085}x^{-1}.

$$n=\frac{0}{-\frac{268}{1085x}}$$

Solve for n (complex solution)

$$n=\frac{i\times 2\times 1085\pi n_{1}x}{268\ln(2)-268\ln(5)}$$

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

$$x\neq 0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x\neq 0\text{, }&\text{unconditionally}\\x=-\frac{i\times \frac{268\ln(2)-268\ln(5)}{1085}n}{2\pi n_{1}}\text{, }n_{1}\in \mathrm{Z}\text{, }n_{1}\neq 0\text{, }&n\neq 0\end{matrix}\right.$$

Solve for x

$$x\neq 0$$