Math Help - Laws of Logarithms HELP!

1. Laws of Logarithms HELP!

I need to use laws of logarithms methods to simplify and evaluate these equation

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

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

I need log to the base 10 to be used preferably

2. Re: Laws of Logarithms HELP!

Originally Posted by Scottrich12
I need to use laws of logarithms methods to simplify and evaluate these equation

5n = 7 x 2n, rearrange and make n the subject
$n=\frac{\log_{10}(7)}{\log_{10}(5)-\log_{10}(2)}$

3. Re: Laws of Logarithms HELP!

That's the answer but how did you get it?

4. Re: Laws of Logarithms HELP!

Originally Posted by Scottrich12
That's the answer but how did you get it?
$\left( {\frac{5}{2}} \right)^n = 7$

5. Re: Laws of Logarithms HELP!

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