Solve for x log base 2 of x+15=4

Problem

(log_2)(x+15)=4

Solution

1. Identify the logarithmic equation and the base, which is 2

2. Rewrite the equation in exponential form by using the definition of a logarithm (log_b)(y)=a⇔b^a=y

2^4=x+15

3. Evaluate the power on the left side of the equation.

16=x+15

4. Isolate the variable x by subtracting 15 from both sides of the equation.

16−15=x

1=x

5. Verify the solution by substituting x=1 back into the original logarithmic expression to ensure the argument is positive.

1+15=16

(log_2)(16)=4

Final Answer

(log_2)(x+15)=4⇒x=1

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