Solve log Equations: The Bridge

What you do

You shape the function y = b^x and watch the graph answer.

Challenges to clear

• With b = 10, the point (3, 1000) appears: log₁₀(1000) = 3.
• Same base: (2, 100) — log₁₀(100) = 2. The bridge works both ways.
• Base 3 now — slide b there.
• Then find the multiplier: x = 4 must read 162. Since 3⁴ = 81, a is 2.

Check yourself

The graph shows y = 10^x. If we start at y=1000 on the vertical axis and move horizontally to the curve, then down to the x-axis, we land on x=3. What does this process define?

Using the same logic, if you start at y=100 on the graph and trace back to the x-axis, what value do you find, and what logarithmic equation does it represent?

• It defines the logarithm: log₁₀(1000) = 3 — correct
• It defines the square root: √1000 = 3
• It defines division: 1000 / 10 = 3
• It defines subtraction: 1000 - 10 = 3
• x=2, representing log₁₀(100) = 2 — correct
• x=3, representing log₁₀(100) = 3
• x=10, representing log₁₀(100) = 10
• x=1, representing log₁₀(100) = 1

Think about it

• log₁₀(1000) = x converts to 10^x = 1000. What is x?