How do you solve #e^(3-5x)=16#?

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Answer 1 · 2018-04-20T08:37:31

#color(blue)(x=(ln(16)-3)/-5~~0.0454822555)#

By the laws of logarithms:

#log_a(b^c)=clog_a(b) \ \ \ \ \ \[1]#

#log_a(a)=1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \[2]#

#e^(3-5x)=16#

Taking natural logarithms of both sides:

Using #[1]#

#(3-5x)ln(e)=ln(16)#

By #[2]#

#3-5x=ln(16)#

Subtract #3#:

#-5x=ln(16)-3#

Divide by #-5#:

#color(blue)(x=(ln(16)-3)/-5~~0.0454822555)#