Thread: 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 = 195^◦C



Thanks in advance

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 = 195^◦C



Thanks in advance

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





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



Solving for n gives



Now you try the 2nd one and remember that

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

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.