How do you use logarithms to solve for x in #5^(x+1)=24#?

1 Answer
Jul 12, 2018

#color(blue)(x~~0.974635869)#

Explanation:

#5^(x+1)=24#

Taking logarithms of both sides:

#ln(5^(x+1))=ln(24)#

Form the laws of logarithms:

#log(a^b)=blog(a)#

#(x+1)ln(5)=ln(24)#

Divide by #ln(5)#

#x+1=ln(24)/ln(5)#

#x=ln(24)/ln(5)-1~~0.974635869#