5^(2x) – 3*5^x = 18 find using natural logs

Step-by-step explanation:

hello :

let : 5^x = t    ... t > 0

note : 5^(2x) = (5^x)²

you have : t²-3t-18=0

(t-6)(t+3) = 0

t-6=0 or t+3=0

t = 6 or t = -3( refused)

but :  5^x = t  so : 5^x = 6

using natural logs : log(5^x) = log6

x log5 =log6

x = log6/log5

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