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

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Answer 1 · 2018-07-12T15:28:43

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

#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#