Solve for x log of 4x+10=3

Problem

(log_)(4*x+10)=3

Solution

1. Identify the base of the logarithm. Since no base is explicitly written, it is assumed to be the common logarithm with base 10

(log_10)(4*x+10)=3

2. Rewrite the logarithmic equation in its equivalent exponential form using the definition (log_b)(y)=x⇔bx=y

10=4*x+10

3. Evaluate the power of 10 on the left side of the equation.

1000=4*x+10

4. Isolate the term containing x by subtracting 10 from both sides of the equation.

990=4*x

5. Solve for x by dividing both sides by 4

x=990/4

6. Simplify the resulting fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2

x=495/2

Final Answer

(log_)(4*x+10)=3⇒x=247.5

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