# Math Help - Simplifying with laws of logarithms

1. ## 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

2. ## Re: Simplifying with laws of logarithms

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 $\ln( e^{t})=t$

3. ## Re: Simplifying with laws of logarithms

How would this be written as log to the base 10?

4. ## Re: Simplifying with laws of logarithms

Originally Posted by Scottrich12
How would this be written as log to the base 10?
you've posted this problem twice ...

Laws of Logarithms HELP!

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