# Simplifying with laws of logarithms

• Oct 10th 2012, 11:45 AM
Scottrich12
Simplifying with laws of logarithms
I am currently studying engineering level 3 NVQ and have been having problems with logarithms, the problems I have been given I don't understand these are:

Use laws of logarithms methods to simplify and evaluate the equation given:

Simplify 5n = 7 x 2n, rearrange and make n the subject

also another problem is

Simplify θ = 250 x e-0.05 x t and make t the subject

and continuing from that:

what is the value of t when θ = 195C

• Oct 10th 2012, 11:57 AM
TheEmptySet
Re: Simplifying with laws of logarithms
Quote:

Originally Posted by Scottrich12
I am currently studying engineering level 3 NVQ and have been having problems with logarithms, the problems I have been given I don't understand these are:

Use laws of logarithms methods to simplify and evaluate the equation given:

Simplify 5n = 7 x 2n, rearrange and make n the subject

also another problem is

Simplify θ = 250 x e-0.05 x t and make t the subject

and continuing from that:

what is the value of t when θ = 195C

For problem number one there are many ways to solve it. Here is one

$5^n=7 \cdot 2^n \iff \frac{5^n}{2^n}=7$

$\left( \frac{5}{2}\right)^n=7$

Now if we take the natural logarithm of both sides we get

$\ln\left( \frac{5}{2}\right)^n=\ln(7) \iff n\ln\left( \frac{5}{2}\right)=\ln(7)$

Solving for n gives

$n=\frac{\ln(7) }{\ln\left( \frac{5}{2}\right)}$

Now you try the 2nd one and remember that $\ln( e^{t})=t$
• Oct 10th 2012, 12:37 PM
Scottrich12
Re: Simplifying with laws of logarithms
How would this be written as log to the base 10?
• Oct 10th 2012, 02:20 PM
skeeter
Re: Simplifying with laws of logarithms
Quote:

Originally Posted by Scottrich12
How would this be written as log to the base 10?

you've posted this problem twice ...

http://mathhelpforum.com/algebra/205...thms-help.html

... in future, please refrain from double posting.