Put \(\displaystyle C=(2+\sqrt {2})^x\) Then \(\displaystyle \frac{1}{C}=\frac{1}{(2-\sqrt {2})^x}\)Chipset3600 said:Hi, I'm having problems to solve this equation, pls help me:
\(\displaystyle \left( 2+\sqrt {2}\right) ^{x}+\left( 2-\sqrt {2}\right) ^{x}=4\)
An exponential equation is an equation in which the variable appears in the exponent. The general form of an exponential equation is y = ab^x, where a and b are constants and x is the variable.
To solve an exponential equation, you can use logarithms or graphing methods. If the equation only has one variable in the exponent, you can isolate the variable by taking the logarithm of both sides. If the equation has multiple variables, you can use graphing methods to find the solution.
To solve this equation, we must first isolate the variable in the exponent. We can do this by subtracting 4 from both sides, then simplifying the left side to get √2^x = 2. Next, we can square both sides to eliminate the square root, giving us 2^x = 4. Finally, we can take the logarithm of both sides to solve for x, which gives us x = 2.
Exponential equations can be used to model population growth, compound interest, radioactive decay, and other natural phenomena that exhibit exponential behavior. They are also commonly used in fields such as economics, biology, physics, and engineering.
Yes, exponential equations can have more than one solution. For example, the equation 2^x = 4 has two solutions, x = 2 and x = -2. However, some exponential equations may not have a real solution, such as in the case of negative numbers raised to a fractional exponent.