Solving Exponential Equation @KasyannoEZMath

This tutorial video explains how to solve the given exponential equation.

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[kfjfkeofitorhf]

9^X-16=65=65+16=81
9^X=81=9^2
X=2
y=1

[kamalerrahali]

We have this possibility too:
a-b=1 and a+b=65
Then a=33 and b=32

[walterwen]

Solving Exponential Equation: 9^x – 16^y = 65; x =?, y = ?
First solution:
First method:
9^x – 16^y = 65 = (5)(13) = (9 – 4)(9 + 4) = 9^2 – 4^2 = 9^2 – 16^1
x = 2, y = 1
Second method:
9^x – 16^y = (3^x)^2 – (4^y)^2 = (3^x – 4^y)(3^x + 4^y) = (5)(13)
3^x – 4^y < 3^x + 4^y; 3^x – 4^y = 5, 3^x + 4^y = 13
2(3^x) = 18, 3^x = 9 = 3^2; x = 2 and (4^x) = 8, 4^y = 4 = 4^1; y = 1
Second solution:
9^x – 16^y = (3^x)^2 – (4^y)^2 = (3^x – 4^y)(3^x + 4^y) = (1)(65)
3^x – 4^y < 3^x + 4^y
3^x – 4^y = 1, 3^x + 4^y = 65; 2(3^x) = 66, 3^x = 33 and 2(4^x) = 64, 4^y = 32
x = log33/log3 = 1 + log11/log3 = 3.183
y = log32/log4 = (log2^5)/(log2^2) = 5/2 = 2.5
Answer check:
x = 2, y = 1
9^x – 16^y = 9^2 – 16^1 = 81 – 16 = 65; Confirmed
x = log33/log3 = 3.183, y = log32/log4 = 2.5
9^x – 16^y = 9^3.183 – 16^2.5 = 1089.82 – 1024 = 65.82; Confirmed
Final answer:
x = 2, y = 1 or x = log33/log3 = 3.183, y = log32/log4 = 2.5