Write the following log in terms of log 3 log 5 and/or log 2

Question

1) log 5/12 

Write the log equations for each then solve using logs

2) x=5 square root (72.43)* 3 square root (.00035)^2 all divided by six square root 5.84

3) 2.35^x=342.7

Answer 1

Remember that log(a/b) = log(a) - log(b), log(ab) = log(a) + log(b), and log(a^b) = b(log(a)).

 

 

 

1.

 

log(5/12)

log(5) - log(12)

log(5) - log(3×4)

log(5) - (log(3) + log(4))

log(5) - log(3) - log(4)

log(5) - log(3) - log(2²)

log(5) - log(3) - 2(log(2))

 

 

 

 

2.

 

It's hard to figure out your equation for this one. I'm not sure if you mean "fifth root" and "cube root" when you write "5 square root" and "3 square root." Also, should that be some number to the x power? If not, then there's no need to use logs.

 

 

 

3.

 

2.34^x = 342.7

log_2.34(342.7) = x

 

Plug that into your calculator to solve for x. If you can only use logs with base 10, then re-write the equation as:

 

log(342.7)/log(2.34) = x