Final Answer:
To condense the given logarithmic expression 3 log₂ (a) + 5 log₂ (b) + 2 log₂ (c) into a single logarithm, we can use the properties of logarithms. The condensed form of the given logarithmic expression is log₂ (a³ b⁵ c²).
Step-by-step explanation:
To condense the given logarithmic expression 3 log₂ (a) + 5 log₂ (b) + 2 log₂ (c) into a single logarithm, we can use the properties of logarithms:
1. n logₐ (x) = logₐ (xⁿ)
2. logₐ (x) + logₐ (y) = logₐ (xy)
Applying these properties, we get:
3 log₂ (a) + 5 log₂ (b) + 2 log₂ (c)
Using property 1 on each term:
log₂ (a³) + log₂ (b⁵) + log₂ (c²)
Now, using property 2 to combine the terms:
log₂ (a³ b⁵ c²)
So, the condensed form of the given logarithmic expression is log₂ (a³ b⁵ c²).
Complete Question:
Condense the given logarithmic expression into a single logarithm 3 log₂ (a) + 5 log₂ (b) + 2 log₂ (c)