SOLUTION: The exercise asks to solve algebraically this equation: 36(1.35)^x=4.35 My work comes up as: 36(1.35)^x-4.35=0 However, I have a key: approx. 8.024 Obviously, my work is wrong, and

Question 427704: The exercise asks to solve algebraically this equation: 36(1.35)^x=4.35 My work comes up as: 36(1.35)^x-4.35=0 However, I have a key: approx. 8.024 Obviously, my work is wrong, and I wonder if I have to solve it using log but I am not sure about the steps. Can you help me to do it, please? Thank you
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
The exercise asks to solve algebraically this equation: 36(1.35)^x=4.35 My work comes up as: 36(1.35)^x-4.35=0 However, I have a key: approx. 8.024 Obviously, my work is wrong, and I wonder if I have to solve it using log but I am not sure about the steps.
..
Usually, when you need to solve a variable that is an exponent, logarithms are required.
36(1.35)^x=4.35
(1.35)^x=4.35/36
taking logs of both sides using the exponent and division rules of logarithms.
xlog(1.35)=log(4.35)-log(36)
x=[log(4.35)-log(36)]/log(1.35)
using calculator
x=-7.0420..
..
Check:
36*1.35^-7.042=4.35
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