Question
10) Solve each equation algebraically. b) 2^2x+1=128 c) 4^3x=8^x-2 a) 2^x=16
Solution
4.4
(223 Votes)
Emma
Advanced ยท Tutor for 1 years
Answer
### a)
### b)
### c)
Explanation
## Step 1: Solve for
in
### Express 16 as a power of 2:
. Therefore,
. Since the bases are equal, the exponents must be equal.## Step 2: Equate the exponents### Set
.## Step 3: Solve for
in
### Express 128 as a power of 2:
. Therefore,
. Since the bases are equal, the exponents must be equal.## Step 4: Equate the exponents### Set
. Subtract 1 from both sides:
. Divide both sides by 2:
.## Step 5: Solve for
in
### Express both sides as powers of 2:
and
. Therefore,
.## Step 6: Equate the exponents### Set
. Subtract
from both sides:
. Divide both sides by 3:
.