# Exponential equation with logs

• I
• Dank2
In summary, the conversation discusses a mathematical equation and its solutions. The equation involves logarithms and can be simplified to reveal solutions of x=0 and x=-1. The process of solving the equation is not straightforward, but the solutions can be easily seen.
Dank2
How can i continue from here, answer is x=0,-2

You lost a factor 4 for 2x 2x.

I would make some common factors of 10x 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.

Dank2
mfb said:
You lost a factor 4 for 2x 2x.

I would make some common factors of 10x 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.
You mean write down 25 as 10log1025?

Last edited:
dont mind the t=0, since it cannot be.

Anyone have a clue how to show it ? it doesn't have to be a proof.

Dank2 said:
Anyone have a clue how to show it ? it doesn't have to be a proof.
If the equation is:
$$\log_{10}\big[25^{x+1}+4^{x+1}-19\cdot 10^x\big]=\log_{10}\big[10^{x+1}\big]$$,
then with some algebra, you can reduce it down to:
$$25^{x+1}+4^{x+1}=\frac{29}{10}\cdot 10^{x+1}$$
and can easily see ##x=0## is a solution and if you plug in ##x=-2##, confirm -2 is a solution also.

## What is an exponential equation with logs?

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.

## How do you solve an exponential equation with logs?

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.

## What are the properties of logarithms used in solving exponential equations with logs?

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.

## What are some real-life applications of exponential equations with logs?

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.

## What are the common mistakes to avoid when solving exponential equations with logs?

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.

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