Exponential Equations (Same Bases)

Authored by Michelle Wilson

Mathematics

9th - 12th Grade

CCSS covered

Used 11+ times

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MATH RESPONSE QUESTION

45 sec • 1 pt

Solve $3^x=3^5$
x = _____

$5$

Mathematical Equivalence

Tags

CCSS.MATH.CONTENT.HSA.SSE.A.2

CCSS.MATH.CONTENT.HSN.RN.A.2

MATH RESPONSE QUESTION

45 sec • 1 pt

Solve.
$36^x=1$
x = _____

$0$

Mathematical Equivalence

Answer explanation

$36^0=1$
Anything raised to the
zero power equals 1

Tags

CCSS.MATH.CONTENT.HSA.SSE.A.2

CCSS.MATH.CONTENT.HSN.RN.A.2

MATH RESPONSE QUESTION

2 mins • 1 pt

8^3x+3 = 8⁶
x = _____

$1$

Mathematical Equivalence

Answer explanation

Solve
3x + 3 = 6
3x = 3
x = 1

Tags

CCSS.MATH.CONTENT.HSA.SSE.A.2

CCSS.MATH.CONTENT.HSN.RN.A.2

MULTIPLE SELECT QUESTION

1 min • 1 pt

Select all expressions that are equivalent to 16.

$2^8$

$2^4$

$4^2$

$8^2$

Tags

CCSS.MATH.CONTENT.HSA.SSE.A.2

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve for x using the same base method.
3^x-20= 27

-7

Answer explanation

$3^{x-20}=27$
$3^{x-20}=3^3$
Now Solve
x - 20 = 3
x = 23

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve 8 = 2^5x+7

x = ⅘

x = ¼

x = -⅘

x = -¼

Answer explanation

$8\ =\ 2^{5x+7}$
$2^3\ =\ 2^{5x+7}$
Now Solve
3 = 5x + 7
-4 = 5x
-4/5 = x

Tags

CCSS.7.EE.B.4A

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve: 2^x = 4^x+1

x = -2

x = 2

x = -3

x = 3

Answer explanation

$2^x=4^{x+1}$
$2^x=\left(2^2\right)^{x+1}$
Now Solve
x = 2x + 2
-x = 2
x = -2

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Sovle for x:
5^{-3x - 1} = 25

x = -1

x = -4

x = -3

x = 1

Answer explanation

$5^{-3x-1}=25$
$5^{-3x-1}=5^2$
Now Solve
-3x - 1 = 2
-3x = 3
x = -1

Tags

CCSS.7.EE.B.4A

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

$9^{5x-2}=\frac{1}{27}$
When solving the given equation, which equation would be used?

$10x-2=-3$

$10x-4=-3$

$5x-2=-3$

$5x-2=1$

Answer explanation

$9^{5x-2}=\frac{1}{27}$
$\left(3^2\right)^{5x-2}=\left(3^{-3}\right)$
Leads to the exponents being
10x - 4 = -3

Tags

CCSS.MATH.CONTENT.HSA.SSE.A.2

CCSS.MATH.CONTENT.HSN.RN.A.2

10.

MATH RESPONSE QUESTION

3 mins • 1 pt

Solve.
$5^{3x+7}=\frac{1}{25}$
x = _____

$-3$

Mathematical Equivalence

Answer explanation

$5^{3x+7}=\frac{1}{25}$
$5^{3x+7}=5^{-2}$
Now Solve
3x + 7 = -2
3x = -9
x = -3

Tags

CCSS.MATH.CONTENT.HSA.SSE.A.2

CCSS.MATH.CONTENT.HSN.RN.A.2

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Exponential Equations (Same Bases)

Solve 3x=353^x=3^53x=35 x = _____

Solve. 36x=136^x=136x=1 x = _____

360=136^0=1360=1 Anything raised to thezero power equals 1

83x+3 = 86x = _____

Solve 3x + 3 = 63x = 3x = 1

Select all expressions that are equivalent to 16.

Solve for x using the same base method.3x-20 = 27

3x−20=273^{x-20}=273x−20=27 3x−20=333^{x-20}=3^33x−20=33 Now Solvex - 20 = 3x = 23

Solve 8 = 25x+7

8 = 25x+78\ =\ 2^{5x+7}8 = 25x+7 23 = 25x+72^3\ =\ 2^{5x+7}23 = 25x+7 Now Solve 3 = 5x + 7-4 = 5x-4/5 = x

Solve: 2x = 4x+1

2x=4x+12^x=4^{x+1}2x=4x+1 2x=(22)x+12^x=\left(2^2\right)^{x+1}2x=(22)x+1 Now Solvex = 2x + 2-x = 2x = -2

Sovle for x:5-3x - 1 = 25

5−3x−1=255^{-3x-1}=255−3x−1=25 5−3x−1=525^{-3x-1}=5^25−3x−1=52 Now Solve-3x - 1 = 2-3x = 3 x = -1

95x−2=1279^{5x-2}=\frac{1}{27}95x−2=271​ When solving the given equation, which equation would be used?

95x−2=1279^{5x-2}=\frac{1}{27}95x−2=271​ (32)5x−2=(3−3)\left(3^2\right)^{5x-2}=\left(3^{-3}\right)(32)5x−2=(3−3) Leads to the exponents being10x - 4 = -3

Solve. 53x+7=1255^{3x+7}=\frac{1}{25}53x+7=251​ x = _____

53x+7=1255^{3x+7}=\frac{1}{25}53x+7=251​ 53x+7=5−25^{3x+7}=5^{-2}53x+7=5−2 Now Solve3x + 7 = -23x = -9x = -3

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Discover more resources for Mathematics

Solve $3^x=3^5$
x = _____

Solve.
$36^x=1$
x = _____

$36^0=1$
Anything raised to the
zero power equals 1

8^3x+3 = 8⁶
x = _____

Solve
3x + 3 = 6
3x = 3
x = 1

Solve for x using the same base method.
3^x-20= 27

$3^{x-20}=27$
$3^{x-20}=3^3$
Now Solve
x - 20 = 3
x = 23

Solve 8 = 2^5x+7

$8\ =\ 2^{5x+7}$
$2^3\ =\ 2^{5x+7}$
Now Solve
3 = 5x + 7
-4 = 5x
-4/5 = x

Solve: 2^x = 4^x+1

$2^x=4^{x+1}$
$2^x=\left(2^2\right)^{x+1}$
Now Solve
x = 2x + 2
-x = 2
x = -2

Sovle for x:
5^{-3x - 1} = 25

$5^{-3x-1}=25$
$5^{-3x-1}=5^2$
Now Solve
-3x - 1 = 2
-3x = 3
x = -1

$9^{5x-2}=\frac{1}{27}$
When solving the given equation, which equation would be used?

$9^{5x-2}=\frac{1}{27}$
$\left(3^2\right)^{5x-2}=\left(3^{-3}\right)$
Leads to the exponents being
10x - 4 = -3

Solve.
$5^{3x+7}=\frac{1}{25}$
x = _____

$5^{3x+7}=\frac{1}{25}$
$5^{3x+7}=5^{-2}$
Now Solve
3x + 7 = -2
3x = -9
x = -3