Step 1 Consider the given equation 27=35x⋅9x2 Step 2 Simplify the equation further as, 27=35x⋅(32)x2 33=35x⋅32x2 33=35x+2x2 Step 3 Equate the exponents. 3=5x+2x2 2x2+5x−3=0 x=−5±52−4(2)(−3)4 x=12,−3 Step 4 Thus, the value of x is x=12,−3

Expert Answer to "27=35x⋅9x2"

High School
Algebra
Algebra I
Algebra foundations

Tiffany Russell

Answered question

2021-12-14

27 = 3^{5 x} \cdot 9^{x^{2}}

Answer & Explanation

Jack Maxson

Beginner2021-12-15Added 25 answers

Step 1
Consider the given equation

27 = 3^{5 x} \cdot 9^{x^{2}}

Step 2
Simplify the equation further as,

27 = 3^{5 x} \cdot {(3^{2})}^{x^{2}}

3^{3} = 3^{5 x} \cdot 3^{2 x^{2}}

3^{3} = 3^{5 x + 2 x^{2}}

Step 3
Equate the exponents.

3 = 5 x + 2 x^{2}

2 x^{2} + 5 x - 3 = 0

x = \frac{- 5 \pm \sqrt{5^{2} - 4 (2) (- 3)}}{4}

x = \frac{1}{2}, - 3

Step 4
Thus, the value of x is

x = \frac{1}{2}, - 3

Wendy Boykin

Beginner2021-12-16Added 35 answers

Rewrite the equation as

3^{5 x} \cdot 9^{x^{2}} = 27

Rewrite 9 as

3^{2}

3^{5 x} \cdot {(3^{2})}^{x^{2}} = 27

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

3^{5 x} \cdot 3^{2 x^{2}} = 27

Use the power rule

a^{m} a^{n} = a^{m + n}

to combine exponents.

3^{5 x + 2 x^{2}} = 27

Create equivalent expression in the equation that all have equal bases.

3^{5 x + 2 x^{2}} = 3^{3}

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

5 x + 2 x^{2} = 3

Solve for x,

x = \frac{1}{2}, - 3

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