use the change of base formula to rewrite the logarithm (write the answer using base e formulas)

Question

y=log₅(x)

Answer 1

y = log base 5 of x

rewritten in exponential form is

x = 5^y

take natural logs of both sides

lnx = yln5

divide both sides by ln5

lnx/ln5 = y

switch sides

y = lnx/ln5

using change of base formula, you get

y = lnx/ln5

where ln means log to the base e= the natural log

Answer 2

y = log₅x

 

Use the relation

 

log_bx = (log_kx)/(log_kb)

 

b = e

k = 5

 

log_ex = (log₅x) / (log₅e)

 

ln(x) = y / log₅e

 

y = (log₅e) ln(x)