We solve: 120 × (1.10)^d > 240 → (1.10)^d > 2 - Deep Underground Poetry
Solving the Equation 120 × (1.10)^d > 240: A Step-by-Step Explanation
Solving the Equation 120 × (1.10)^d > 240: A Step-by-Step Explanation
If you’ve ever wondered how to solve exponential inequalities like 120 × (1.10)^d > 240, you’re in the right place. In this article, we’ll break down the process clearly and show you how to solve (1.10)^d > 2, a simplified version of the original inequality, using fundamental mathematical principles.
Understanding the Context
Why This Equation Matters
Exponential functions model real-world phenomena such as compound interest, population growth, and radioactive decay. Understanding how to solve equations of the form a × b^d > c helps in finance, science, and engineering. Our focus here is solving (1.10)^d > 2, a common form that appears when analyzing growth rates.
Step 1: Simplify the Inequality
Image Gallery
Key Insights
Start with the original inequality:
120 × (1.10)^d > 240
Divide both sides by 120:
(1.10)^d > 2
Now we solve this exponential inequality — a key step toward understanding how the base (1.10) grows over time d.
Step 2: Solve the Corresponding Equation
🔗 Related Articles You Might Like:
📰 Business Credit Score Check 📰 Average Auto Loan Interest Rate 📰 What Does Dba Mean in Business 📰 Ragazzi Meaning 738029 📰 Your Tiny Sleep Switch Hits The Panic Button 1250095 📰 How To Properly Complete Your 1099 R Formyour Step By Step Guide Inside 4385236 📰 Youll Never Believe What Sand Dabs Do When The Tide Hits 8976012 📰 The City Tv Show 3869832 📰 Alexandra Stan 1079627 📰 This Red Lace Dress Will Make You The Center Of Attention Every Time You Wear It 2676511 📰 Calculate Savings Account 4911558 📰 Watch Scary Movie 9931385 📰 The Hidden Gem Behind Every Good Staircasethis Newel Post Shocked Us 3857492 📰 Hcc Share Price Soars Shocking Rise Surprises Wall Street Investors 4100039 📰 Filmes Star Wars 540191 📰 Eden Prairie 1775459 📰 Adachis Dark Legacy Unraveled The Shocking Crimes That Shook The Entertainment World 5708009 📰 Shocking Update November 2025 Mortgage Rates Jump 12Heres How It Could Impact Your Home Loan 1209481Final Thoughts
To isolate the exponent d, first convert the inequality into an equation by changing the “>” to “=”:
(1.10)^d = 2
This helps us find the threshold value of d beyond which the inequality holds.
Step 3: Take the Logarithm of Both Sides
Use logarithms to bring the exponent down:
Take natural logarithm (ln) or common logarithm (log) — either works.
Apply ln:
ln((1.10)^d) = ln(2)
Use the logarithmic identity: ln(a^b) = b·ln(a)
This gives:
d · ln(1.10) = ln(2)
Step 4: Solve for d
Now isolate d:
d = ln(2) / ln(1.10)
Using approximate values:
- ln(2) ≈ 0.6931
- ln(1.10) ≈ 0.09531
