Find the exact solution of the exponential equations in terms of logarithms.

Question

e^0.8x = 4

10(1.375)^19t = 70

Answer 1

e^0.8x = 4. Take the natural log of both sides to get

0.8x = ln4

x= ln4/0.8

10(1.375)^19t = 70

(1.375)^19t = 70/10

1.375^19t = 7 Now can take log base 10 or natural log of both sides-will use natural log

ln(1.375)^19t = ln 7. Now since loga^x = xloga

19t(ln1.375) = ln 7

19t= (ln7)/(ln1.375)

t= (ln7)/19(ln1.375)