Question

Solve the following equations for x and y 7^x+5^y=74 and 7^x+1 - 5^y+1=218​

Answer 1

7

x

+5

y

=74 ____ (1)

7

x+1

−5

y+1

=218

7

x

.7−5

y

.5=218 __ (2)

Leta=7

x

;b=5

y

a +b = 74

a = 74 - b ___ (3)

7a -5b = 218 ___ (4)

Put (a) in (4)

7 (74 - b) -5b = 218

518 - 7b -5b = 218

518-218 = 12b

b = 300/12

b = 25

Put 'b' in (3)

a = 74 - 25 = 49

but a=7

x

7

x

=49=7

2

∴x=2

b = 25

5

y

=5

2

∴y=2

Answer 2

2. $7 {}^{x} + {5}^{y} = 74$

$think \: x \: as \: 1 \: y \: as \: 2$

${7}^{1} + {5}^{2} = 74$

$12 {}^{3} = 74$

$36 = 74$

$\frac{74}{36}$

$\frac{37}{18}$