Exponential Equations

Exponential equations with a common base. In MathBound, the free Algebra I adventure game, Same-Base Sam asks these problems, and the only way past is to solve them.

Part of Exponents and Exponential Functions: chapter 7 of the standard course.

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10 questions, no sign-up, nothing saved. Climbs from the basics to harder questions.

What you will practice

Equations with a Common Base. Solve b^x = b^n with a whole-number power, from a table, or find the first whole year a model passes a level.

Worked examples

Made by the game’s own question engine. Try each one, then open its steps.

Example 1 · Equations with a Common Base

Solve:

4^{x} = 1

$x = 4$
$x = 1$
$x = \frac{1}{4}$
$x = 0$

Show the worked steps

$Any$ $non-zero$ $number$ $to$ $the$ $power$ $0$ $is$ $1 : 4^{0} = 1.$
$So$ $x = 0.$

Answer: $x = 0$

Example 2 · Equations with a Common Base

The

table

shows

y = 4 (3)^{x} .

For

what

value

of

x

is

y = 972 ? x y 041122363108

$x = 4$
$x = 5$
$x = 324$
$x = 81$

Show the worked steps

$Keep$ $multiplying$ $by$ $3 : 4, 12, 36, 108, 324, 972 .$
$y = 972$ $when$ $x = 5 .$

Answer: $x = 5$

Example 3 · Equations with a Common Base

Solve:

2 \cdot 3^{x} = 54

$x = 27$
$x = 4$
$x = 3$
$x = 2$

Show the worked steps

$Divide$ $by$ $2 : 3^{x} = 27 .$
$27 = 3^{3},$ $so$ $x = 3 .$

Answer: $x = 3$

Where it is in your textbook

Textbook	Lessons
Standard course	7.7
Big Ideas Math Algebra 1	6.5
Big Ideas Math Algebra 1 (2022)	6.5
Carnegie Learning Algebra I	M3 1.2
CPM Core Connections Algebra	10.2.1, 11.3.5
enVision Algebra 1	6-1
enVision Algebra 1 (2024)	6-1
Glencoe Algebra 1	7-3
Reveal Algebra 1	8-7

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