show that each expression is equivalent to ln8

Question

(log₁₀2 + log₁₀4) / log₁₀ e

 

I got as far as: log₁₀8/log_10e

but then I don't know how to simplify log₁₀e and end up getting ln8 as an answer

Answer 1

You are correct as far as you have gone! This exemplifies the change of base formula

 

log_b(x) = log_d(x) / log_d(b)

 

In the  given x = 8, b = e, and d = 10

 

log_e = ln

Answer 2

You need the change of base formula.      There are various ways to express this formula.  Here is one:

 

  ln(x)   =   log₁₀(x) / log₁₀(e)

 

  Thus      ln(8) =  log₁₀(8) / log₁₀(e)

 

 

   More generally        log_b(x) =    log₁₀(x) / log₁₀(b)   for any base b.