- #1
Dank2
- 213
- 4
How can i continue from here, answer is x=0,-2
You mean write down 25 as 10^{log1025?}mfb said:You lost a factor 4 for 2^{x} 2^{x}.
I would make some common factors of 10^{x} and from there on say that you can see the solution. There is no nice way to solve this as far as I can see.
If the equation is:Dank2 said:Answers are x=0, x=-1.
Anyone have a clue how to show it ? it doesn't have to be a proof.
An exponential equation with logs is an equation that involves both exponential functions and logarithmic functions. These equations are used to model situations where a quantity is growing or decaying at a constant rate.
To solve an exponential equation with logs, you can use the properties of logarithms to rewrite the equation in a simpler form. Then, you can use algebraic techniques to isolate the variable and solve for its value.
The properties of logarithms used in solving exponential equations include the product rule, quotient rule, power rule, and change of base formula. These properties allow you to manipulate the logarithmic expressions and simplify the equation.
Exponential equations with logs are commonly used in finance, biology, and physics. In finance, these equations can be used to model compound interest and population growth. In biology, they can be used to model the decay of radioactive elements. In physics, they can be used to model the growth or decay of energy in a system.
Some common mistakes to avoid when solving exponential equations with logs include forgetting to apply the properties of logarithms correctly, making algebraic errors, and forgetting to check for extraneous solutions. It is important to carefully follow the steps and double-check your work to avoid these mistakes.