We have hundreds of course questions with personalized recommendations + Account 100% premium
To solve the problem, we'll follow these steps:
Now, let's work through each step:
Step 1: Combine the logarithms using the product rule:
.
Step 2: Convert the logarithmic equation to an exponential equation:
.
Step 3: Simplify the quadratic equation:
:
.
.
Divide by 3 to simplify:
.
Solve this equation using the quadratic formula:
The quadratic formula is .
Here, , , and .
Calculate the discriminant:\
.
Now, calculate :
.
.
Calculating this gives approximately .
Step 4: Verify that to be in the domain.
Since this is true, the valid solution is within the domain, confirming:
Therefore, the solution to the problem is .
\( \log_{10}3+\log_{10}4= \)
Get unlimited access to all 18 Rules of Logarithms questions, detailed video solutions, and personalized progress tracking.
Unlimited Video Solutions
Step-by-step explanations for every problem
Progress Analytics
Track your mastery across all topics
Ad-Free Learning
Focus on math without distractions
No credit card required • Cancel anytime