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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