We solve: 120 × (1.10)^d > 240 → (1.10)^d > 2

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

We solve: 120 × (1.10)^d > 240 → (1.10)^d > 2

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:

📰 Attention All Trainers—Next Pokémon Game Drops SHOCKINGly New Legends! 📰 TCG & Battle New Pokémon! The Next Game Breaks All Expectations—Here’s How! 📰 Is This the Most Anticipated Next Pokémon Game Ever? Major Secrets Inside! 📰 The King Bed Frame Thats Taking Bedrooms By Storm Landed 📰 The King Chess Piece That Dominates Every Game Watch That Instant Win 📰 The King Chess Piece Thats Revolutionizing Strategy Dont Miss This Mind Blowing Trick 📰 The King Edward Love Chair Thats Changing How We Decorate Inside This Timeless Masterpiece 📰 The King Of Christmas Trees How This Giant Outshines All Others This Season 📰 The King Of Memes Explodes Onlineheres What Made This Meme Unstoppable 📰 The King Of Thrones Season 8 What Viewers Are Obligated To Watch Before It Ends 📰 The King Shepherd German Shepherd Why This Breed Dominates Dog Owners Hearts 📰 The Kingdom Come Comic Thats Taking Gamers By Storm Dont Miss These Reveals 📰 The Kingdom Of Hearts Revealed Secrets That Will Break Your Heart And Your Heartstrings 📰 The Kingdra Weakness No One Talks About Lead Your Rivals To Defeat 📰 The Kingpin Marvel Launch That Exploded Online What Youre Missing 📰 The Kingpin Vs Spider Man Will The Hero Rise Or Crumble Under Pressure 📰 The Kit Bernard Foster Miracle Everyone Talked About What Happened Next Shocked The Internet 📰 The Klass Of Villainy Why Kraven Is The Most Made Up Character In Pop Culture Luck

Final 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