How to solve an exponential equation with two different bases

👉 Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspond to the base of the exponential part of the equation, so that the log cancels out the exponential function, leaving out only the exponent.

If we can make the base of both sides of the equation to be equal, we then equate their respective exponents and then solve.

Organized Videos:
✅Solve Exponential Equations
✅Solve Exponential Equations | Learn About
✅Solve Exponential Equations with a Calculator
✅Solve Exponential Equations with Fractions
✅Solve Exponential Equations | Easy
✅Solve Exponential Equations with e
✅Solve Exponential Equations with Logarithms
✅Solve Exponential Equations without a Calculator

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[ddouglas]

One thing I did to teach my brother one to one for his Algebra 2 class is I gave him a problem like this

2^2x+4=2^x+3

To demonstrate why we can easily drop the base

(2x+4)log2=(x+3)log2

Then we divided out log2 and got

2x+4=x-3

Did some basic algebra and got x=7.

[iTerracottaPie]

Dear Mr. Brian,


I would like to thank you first for your extraordinary explanation of mathematics!


I'm really facing hard times solving this problem; i checked your channel for help but didn't find relevant one, so here it is:

solve the equation e^2x = 2^x−4

Many thanks ❤️

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[EthanRMus]

Thank you! Learning decibels for music production and this helped me be able to solve those equations.