Full solution

\left(\frac{1,07 \times 10^{-1}}{1,56 \times 10^{-2}}\right)^{x}=\left(\frac{1,32}{2,89}\right)

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6

058

Calculate Division: Now, calculate the division of $1.07$ by $1.56$ . $\newline$ $1.07 / 1.56 \approx 0.6859$
Simplify Equation: Next, simplify the right side of the equation by dividing $1.32$ by $2.89$ . $\frac{1.32}{2.89} \approx 0.4567$
Multiply and Simplify: We now have the equation $(0.6859 \times 10)^{x} = 0.4567$ . Simplify the left side by multiplying $0.6859$ by $10$ . $0.6859 \times 10 = 6.859$
Take Logarithm: The equation is now $6.859^{(x)} = 0.4567$ . $\newline$ To solve for $x$ , take the logarithm of both sides. $\newline$ $log(6.859^{(x)}) = log(0.4567)$
Move Exponent: Using the property of logarithms, move the exponent $x$ in front of the log. $x \cdot \log(6.859) = \log(0.4567)$
Calculate Logarithms: Now, calculate the logarithms. $\log(6.859) \approx 0.8365$ and $\log(0.4567) \approx -0.3404$
Divide and Solve: Divide both sides by $\log(6.859)$ to solve for $x$ . $\newline$ $x = \frac{\log(0.4567)}{\log(6.859)}$ $\newline$ $x \approx \frac{-0.3404}{0.8365}$
Final Calculation: Finally, calculate the division to find the value of $x$ . $x \approx -0.3404 / 0.8365 \approx -0.407$