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Graphing exponential

100

f(x)=(5/2)^x

^{what is the y-intercept} 

(0,05)

200

f(x)=(2/3)^x

^{whats the range} 

y>0

300

f(x)=(1/2)^x

^{whats the asymptote} 

y=0

400

f(x)=3^x

^{whats the range} 

y>0

500

f(x)=2^x 

^{what's the y-intercept}

(0,1)

Solving exponential equations

100

solve 5⁴ⁿ⁺⁵=5^n-7

12/3

200

solve 3^k x 3^k+2=3^5k`1

k=1

300

4^y+2=16^y-3

y=8

400

7^4x+11=1/7

x=-3

500

9^2x+4 x 9^2x=1/81

x=-2/3

Converting log to exponential or exponential to log

100

log₇1=0

7¹=9

200

log₉27=3/2

9²=3/2

300

36^1/2=6

log₃₆ 6=1/2

400

8^4/3 =16

log₈ 16=4/3

500

12¹=12

log₁₂ 12=1

Condensing logs/exponential

100

log₃ 4+log₃ y +1/2 x log₃ 49

log³ 28g

200

1/3(log₅ 8+log₅ 27)-log₅ 3

log₅ 2

300

2xlog 6-log 9

log 4

400

7x log₄u-3 x log ₄ v²

log₄ (u⁷/v⁶)

500

4 x log₄ a + 2 x log₄ b

log₄ (a⁴b²)

Expanding Logs/exponential

100

log₆ (xyz⁴ )

log₆ x+log₆y+4 log₆z

200

log₂ (y/z⁵)²

2(log₂ y-z⁵)

300

log₃ ⁴√ m⁵ n²

1/4(5 log₃ m +2 log3 n)

400

log₄(a⁹/b)

9log₄a-log₄ b

500

log₈ (mn)²

log₈m+2 log₈ n