How do you solve #e^(p+10)+4=18#?

1 Answer
Aug 17, 2016

Answer:

#p = ln(14)-10 ~~-7.3609#

Explanation:

The base-#a# logarithm of #x#, denoted #log_a(x)#, is the power which #a# must be taken to for #a^(log_a(x))# to equal #x#. Because of this, it should be quite clear that for any #x#, we have #log_a(a^x) = x#, as #x# is the power which #a# must be taken to to obtain #a^x#.

Using this, along with the convention that the natural log #ln(x)# is the base-#e# logarithm of #x#:

#e^(p+10) + 4 = 18#

#=> e^(p+10) = 14#

#=> ln(e^(p+10)) = ln(14)#

#=> p+10 = ln(14)#

#:. p = ln(14)-10 ~~-7.3609#