How do you solve #5(2)^(2x)-4=13#?

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Answer 1 · 2017-01-27T21:42:48

Please see the explanation.

Add 4 to both sides:

#5(2)^(2x) = 17#

Divide both sides by 5:

#(2)^(2x) = 17/5#

Use the natural logarithm on both sides:

#ln((2)^(2x)) = ln(17/5)#

Use the property #ln(a^b) = (b)ln(a)#

#(2x)ln((2)) = ln(17/5)#

Divide both sides by 2ln(x):

#x = ln(17/5)/(2ln(2))#

check:

#5(2)^(2(ln(17/5)/(2ln(2)))) - 4 = 13#

#5(2)^((ln(17/5)/(ln(2)))) - 4 = 13#

#5(2)^((log_2(17/5)) - 4 = 13#

#5(17/5) - 4 = 13#

#17 - 4 = 13#

#13 = 13#

#x = ln(17/5)/(2ln(2))# checks.