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Chapter 13: Problem 30

Write as the sum or difference of logarithms and simplify, if possible. Assume all variables represent positive real numbers. $$\log _{2} 2^{9}$$

Short Answer

Expert verified
Applying the logarithm property \(log_a a^x = x\), we have \(log_{2} 2^9 = 9\). The expression is already simplified, and the final answer is 9.

Step by step solution

01

Use the property of logarithms \(log_a a^x = x\), where in our case, the base (a) is 2 and the exponent (x) is 9. So we have \(log_{2} 2^9 = 9\). #Step 2: Simplify the expression#

The expression \(log_{2} 2^9 = 9\) is already simplified as a single number. There are no other logarithms to write it as a sum or difference, and no further simplification is required. The final answer is 9.

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