Hi,

the idea is to have the base numbers the same ⇒ Exponents are Equal

a) 7^x=49   ⇒  7^x = 7^2   ⇒  x = 2

b) 243 = 9^2x+1  ⇒    ⇒  5 = 2(2x+1), x = 3/4

c) 2^2x * 4^4x +8 = 64  ⇒  , x= -1

d)9^x-1 * 81 ^2x-1 = 27^3x-2  ⇒  x = 0  

Answer by lwsshak3(11628)   (Show Source): You can put this solution on YOUR website!
 Solve the following exponential equations:

a) 7^x=49

7^x=7^2

x=2

..

b) 243 = 9^(2x+1)

3^5=3^2^(2x+1)

3^5=3^(4x+2)

4x+2=5

4x=3

x=3/4

..

c) 2^2x * 4^(4x +8) = 64

2^2x * 2^2(4x+8) =2^6

2^2x*2^(8x+16)=2^6

2^(10x+16)=2^6

10x+16=6

10x=-10

x=-1

..

d)9^(x-1) * 81 ^(2x-1) = 27^(3x-2)

9^(x-1) * 9^2 ^(2x-1) = 3^3^(3x-2)

9^(x-1) * 9^(4x-2) = 3^3^(3x-2)

3^2^(x-1) * 3^2 ^(4x-2) = 3^3^(3x-2)

3^(2x-2)*3^(8x-4)=3^(9x-6)

3^(10x-6)=3^(9x-6)

10x-6=9x-6

x=0



 

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