Final answer:
To combine 2log₂ 3 + log₂ 5 into a single logarithm, we first convert 2log₂ 3 to log₂(3^2), then add log₂ 5 to get log₂(45).
Step-by-step explanation:
The question asks us to combine the following logarithmic expressions into a single logarithm and simplify: 2log₂ 3+log₂ 5. By using the properties of logarithms, we can solve this problem. First, we use the property that states the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number (log(x^y) = y · log(x)).
So, 2log₂ 3 becomes log₂ (3^2). Now the expression is log₂ (3^2) + log₂ 5. Next, we apply the property that the logarithm of a product of two numbers is the sum of the logarithms of the two numbers (log(xy) = log(x) + log(y)). Therefore, log₂ (3^2) + log₂ 5 simplifies to log₂ (9 · 5).
Finally, we multiply 9 by 5 to get 45, and our single logarithm is log₂ 45. This is the simplified form of the original expression.