# Hi, I have a problem. Its logarithms.

• Tikoonmunci
In summary, the conversation is about solving the equation 325*(0.8)^t=5 and the suggestion to use logarithms to solve it. The conversation also discusses how to isolate the unknown in the equation and the use of logarithmic properties to solve it. The conversation ends with a playful exchange about being the "sheriff" of the internet.
Tikoonmunci
325*(0.8)^t=5

You should probably take a logarithm. What are you having trouble with? You have to explain where you're getting stuck

Tikoonmunci said:
325*(0.8)^t=5

Since you say "it's logarithms", you probably already know what you should do- the whole point of logarithms is that they "inverse" to exponentials: log(a^x)= x log(a), getting the "x" out of the exponent.

Rather that take the logarithm immediately (which is possible), I would reduce this to a "bare" exponential by dividing both sides by 325: (0.8)^t= 5/325= 1/65. Now take the logarithm of both sides. (Any logarithm will do. Common log (base 10) or natural log (base e), which are on a calculator, will give the same answer.)

Tikoonmunci said:
325*(0.8)^t=5

Like in any equation you have isolate the unknown.

This looks to be High School level. You are properly familar with the function

$$y(t) = b \cdot a^t$$ ?

Then if you have to find t you use standard elimation such as : $$\frac{y(t)}{b} = a^t$$

take the logaritm on both sides of equality and use this fact to isolate t (remember $$a^t = t \cdot log(a))$$

Then the eqn is solved my friend :)

Susanne217 said:
$$a^t = t \cdot log(a))$$

Correction, $$log(a^t)=tlog(a)$$

Mentallic said:
Correction, $$log(a^t)=tlog(a)$$

bang you got me chief :D

I'll let you off this time, but you just better be getting the heck on outta here and never let me see your face around these parts of town again, you hear!?

Mentallic said:
I'll let you off this time, but you just better be getting the heck on outta here and never let me see your face around these parts of town again, you hear!?

Well I didn't know there was a new sherif in these here parts of the Intermerwebs :)

Actually I'm still a chief. I keep civility by day, and smoke my peace pipe by night. Oh and I happen to help with homework every now and again

## What are logarithms and how do they work?

Logarithms are mathematical functions that are used to solve exponential equations. They represent the power to which a base number must be raised to equal a given number. For example, the logarithm base 2 of 8 is 3, because 2 to the power of 3 equals 8.

## Why are logarithms useful?

Logarithms are useful because they allow us to easily solve complex exponential equations, and they can be used to convert between different number systems, such as converting a multiplication problem into an addition problem.

## How do I solve a logarithmic equation?

To solve a logarithmic equation, you can use the properties of logarithms to rewrite the equation into a simpler form. Then, you can solve for the variable by isolating it on one side of the equation and using the inverse operation of exponentiation.

## What is the difference between a natural logarithm and a common logarithm?

A natural logarithm, denoted as ln, has a base of e, which is a mathematical constant approximately equal to 2.718. A common logarithm, denoted as log, has a base of 10. The values of these two logarithms may differ, but they both follow the same logarithmic properties.

## Can you give an example of a real-life application of logarithms?

Logarithms are used in various fields such as science, finance, and engineering. A common application is in measuring the loudness of sound, where the decibel scale uses logarithms to represent the intensity of sound waves. Logarithms are also used in data compression, pH levels in chemistry, and the Richter scale for measuring the magnitude of earthquakes.

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