You can take the log of the left and right hand side, and then apply the <span>logarithm rules:
log(a</span>ˣ) = x·log(a)
log(ab) = log(a) + log(b)
log(9^(x-1) * 2^(2x+2)) = log(6^(3x))
log(9^(x-1)) + log(2^(2x+2)) = 3x log(6)
(x-1) log(9) + (2x+2) log(2) - 3x log(6) = 0
x(log9 + 2log2 - 3log6) = log9 - 2log2
x = (log9 - 2log2) / (log9 + 2log2 - 3log6)
simplifying by writing log9 = 2log3 and log6 = log2+log3
x= 2(log3 - log2) / (2log3 + 2log2 - 3log2 - 3log3) =
x= -2(log3 - log2) / (log3 + log2) = -2 log(3/2) / log(6)
So 6^x = 4/9
Answer:
- 4
Step-by-step explanation:
Using the rule of exponents
• 
× 
⇔ 
• 
⇔ 
= 
= 
and right side
= 
× 
Hence
= 
× 
= 
Equating exponents on both sides gives
a + 10 = - 2a - 2 ( add 2a to both sides )
3a + 10 = - 2 (subtract 10 from both sides )
3a = - 12 ( divide both sides by 3 )
a = - 4
Answer:
203.5 N
Step-by-step explanation:
Force = mass × acceleration
F = ma
F = (55 kg) (3.7 N/kg)
F = 203.5 N
Expanded Notation Form:
7,000
+ 400
+ 20
+ 0
Expanded Factors Form:
7 × 1,000
+ 4 × 100
+ 2 × 10
+ 0 × 1
Expanded Exponential Form:
7 × 103
+ 4 × 102
+ 2 × 101
+ 0 × 100
Word Form:
seven thousand four hundred twenty
