Solving/Properties Log and Exponentials Review Date:

1) Graph 𝑓(𝑥) = 3(𝑥+2)

2) Graph ℎ(𝑥) = 𝑙𝑜𝑔4(𝑥 − 1)

3) Graph 𝑔(𝑥) = (12)

𝑥

4) Convert to an exponential equation: a) log 3𝑥 = −5

b) Convert to logarithmic expression

𝑦 = 3𝑏

5) a)Solve 𝑙𝑜𝑔2𝑥 = 3

b) Solve 3𝑥+1 = 1

27

6) Solve 𝑙𝑜𝑔9(3𝑥 − 4) − 𝑙𝑜𝑔9 (1 − 5𝑥) = 0

Solving/Properties Log and Exponentials Review Date:

1) Graph 𝑓(𝑥) = 3(𝑥+2)

2) Graph ℎ(𝑥) = 𝑙𝑜𝑔4(𝑥 − 1)

3) Graph 𝑔(𝑥) = (12)

𝑥

4) Convert to an exponential equation: a) log 3𝑥 = −5

b) Convert to logarithmic expression

𝑦 = 3𝑏

5) a)Solve 𝑙𝑜𝑔2𝑥 = 3

b) Solve 3𝑥+1 = 1

27

6) Solve 𝑙𝑜𝑔9(3𝑥 − 4) − 𝑙𝑜𝑔9 (1 − 5𝑥) = 0

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7) Expand using properties of logs and rational exponents

log3 √𝑥2𝑦35

8) Solve 2𝑙𝑜𝑔43𝑥 = 𝑙𝑜𝑔4(27) 9) Solve 𝑙𝑜𝑔7√𝑥2 + 2 = 1

10) Expand using properties of logs and rational exponents

𝑙𝑜𝑔𝑤121𝑥3

4√𝑥

11) Condense to express as a single logarithm.

𝑙𝑜𝑔𝑐6 + 2𝑙𝑜𝑔𝑐𝑥 − (3𝑙𝑜𝑔𝑐5 + 5𝑙𝑜𝑔𝑐𝑥2)

12) Solve 2 + 𝑒𝑥+2 = 12

7) Expand using properties of logs and rational exponents

log3 √𝑥2𝑦35

8) Solve 2𝑙𝑜𝑔43𝑥 = 𝑙𝑜𝑔4(27) 9) Solve 𝑙𝑜𝑔7√𝑥2 + 2 = 1

10) Expand using properties of logs and rational exponents

𝑙𝑜𝑔𝑤121𝑥3

4√𝑥

11) Condense to express as a single logarithm.

𝑙𝑜𝑔𝑐6 + 2𝑙𝑜𝑔𝑐𝑥 − (3𝑙𝑜𝑔𝑐5 + 5𝑙𝑜𝑔𝑐𝑥2)

12) Solve 2 + 𝑒𝑥+2 = 12

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