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 5^{n} = 7 x 2^{n}, 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 = 195^{◦}C

Thanks in advance

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 5^{n} = 7 x 2^{n}, 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 = 195^{◦}C

Thanks in advance

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

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

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

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

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

Solving for n gives

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

Now you try the 2nd one and remember that $\displaystyle \ln( e^{t})=t$

Re: Simplifying with laws of logarithms

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

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.