How do you solve #3^(2x) = 75#?

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Answer 1 · 2016-01-29T10:26:25

#x=1.9649735207179#

Start from the given equation:

#3^(2x)=75#

Take the logarithm of both sides of the equation

#log_10 3^(2x)=log_10 75#

#(2x)*log_10 3=log_10 75#

divide both sides of the equation by #log_10 3#

#((2x)*log_10 3)/log_10 3=log_10 75/log_10 3#

#((2x)*cancel(log_10 3))/cancel(log_10 3)=log_10 75/log_10 3#

#2x=log_10 75/log_10 3#

#x=1/2*log_10 75/log_10 3# the exact value

#color (red)(x=1.9649735207179# the calculator value

Check: at #x=1.9649735207179#

#3^(2x)=75#

#3^((2*(1.9649735207179)))=75#

#75=75#

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