SOLUTION: Solve the following exponential equations: a) 7^x=49 b) 243 = 9^2x+1 c) 2^2x * 4^4x +8 = 64 d)9^x-1 * 81 ^2x-1 = 27^3x-2

Algebra ->  Exponents -> SOLUTION: Solve the following exponential equations: a) 7^x=49 b) 243 = 9^2x+1 c) 2^2x * 4^4x +8 = 64 d)9^x-1 * 81 ^2x-1 = 27^3x-2      Log On


   

Question 634606: Solve the following exponential equations:
a) 7^x=49
b) 243 = 9^2x+1
c) 2^2x * 4^4x +8 = 64
d)9^x-1 * 81 ^2x-1 = 27^3x-2
Found 2 solutions by ewatrrr, lwsshak3:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

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  ⇒  3%5E5+=+3%5E%282%282x%2B1%29%29  ⇒  5 = 2(2x+1), x = 3/4

c) 2^2x * 4^4x +8 = 64  ⇒  2%5E%282x%29%2A2%5E%282%284x%2B8%29%29+=+2%5E%2810x+%2B+16%29=+2%5E6, x= -1

d)9^x-1 * 81 ^2x-1 = 27^3x-2  ⇒ 3%5E%2810x-6%29+=+3%5E%289x-6+%29 x = 0

Answer by lwsshak3(11628) About Me  (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