# Some tricky exponentioal equations

• xortan
In summary, Changing the base to 3x instead of 1x and getting: 3^{7x} \cdot (3^3)^x = 3^{7x + 3x} = 3^{10x} seems fishy and doesn't work correctly.
xortan

## Homework Statement

e^(4x-5)=9e^(x+5)

log rules

## The Attempt at a Solution

I have tried this one a few times using slightly different methods and getting 2 answers and neither of them seem to be working when i plug them back into the equation.

Here is my first method...

1. Divide out the e^(x+5) so i get e^(4x-5)/e^(x+5) = 9

2. Take the natural log of everything so i end up with

(4x-5)lne/(x+5)lne = ln 9

3. After doing the algebra i got the answer to be 8.87 (rounded to 3 sig figs), but it wasnt checking out when i plugged it back into the equation

Here is my second method...

1. I just started going crazy with the natural logs getting

(4x-5)lne - (x+5) ln 9e

The ln9e don't quite sit right with me tho, however after doing the algebra i get x=-10, this doesn't seem to check out either...please help!

(3^7x)(27^x)=9

logs

## The Attempt at a Solution

Alright well since i know that they are all powers of 3 i changed the bases so the equation became

(3^7x)((3^3)x)=3^2

Then i just looked at the exponents and ended up with

21x^2 = 2

Did the algebra and this one isn't working in the orignal equation either >.<

Last edited:
xortan said:

## Homework Statement

e^(4x-5)=9e^(x+5)

log rules

## The Attempt at a Solution

I have tried this one a few times using slightly different methods and getting 2 answers and neither of them seem to be working when i plug them back into the equation.

Here is my first method...

1. Divide out the e^(x+5) so i get e^(4x-5)/e^(x+5) = 9

2. Take the natural log of everything so i end up with

(4x-5)lne/(x+5)lne = ln 9
This part is incorrect. The natural log doesn't quite work like that. Before you take natural logs, you'll want to simplify:
$$\frac{e^{4x-5}}{e^{x+5}} = e^{(4x - 5) - (x + 5)} = e^{3x - 10}$$
Then you have e^(3x-10) = 9, and you can take the ln of both sides there.

3. After doing the algebra i got the answer to be 8.87 (rounded to 3 sig figs), but it wasnt checking out when i plugged it back into the equation

Here is my second method...

1. I just started going crazy with the natural logs getting

(4x-5)lne - (x+5) ln 9e

The ln9e don't quite sit right with me tho, however after doing the algebra i get x=-10, this doesn't seem to check out either...please help!

(3^7x)(27^x)=9

logs

## The Attempt at a Solution

Alright well since i know that they are all powers of 3 i changed the bases so the equation became

(3^7x)((3^3)x)=3^2

Then i just looked at the exponents and ended up with

21x^2 = 2
Seems a little fishy here. You changed everything to base 3 right, but then you should get:
$$3^{7x} \cdot (3^3)^x = 3^{7x} \cdot 3^{3x} = 3^{7x + 3x} = 3^{10x}$$

So then 3^(10x) = 3^2, which means x = ...

Did the algebra and this one isn't working in the orignal equation either >.<

Thank you so much it just clicked..

I LOVE this site, got my finals right around the corner and this was only problem i was having with exponentioals, thank you i should be able to complete the rest of my assignment with ease :D

aye, no problem.. good luck!

Just be sure to remove that "o" from "exponentioal" if you want full marks

## What is an exponential equation?

An exponential equation is an equation in which the variable appears in the exponent, rather than the base. It is commonly written in the form y = ab^x, where a is a constant and b is the base.

## How do I solve an exponential equation?

To solve an exponential equation, you can use logarithms or take the logarithm of both sides of the equation. Another method is to use trial and error by plugging in different values for the variable until you find the solution.

## What is the difference between exponential and logarithmic equations?

An exponential equation is written in the form y = ab^x, while a logarithmic equation is written in the form y = log(base a) x. The two are inverse functions of each other, meaning they "undo" each other when used together.

## Can an exponential equation have a negative exponent?

Yes, an exponential equation can have a negative exponent. This indicates that the base is being raised to a negative power, which is equivalent to taking the reciprocal of the base raised to the corresponding positive power.

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

Exponential equations are commonly used in finance, population growth, radioactive decay, and other fields where quantities grow or decay at a constant rate. They can also be used to model the spread of diseases and the growth of bacteria cultures.

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