What is the answer to 2^{6x+3}x4^{3x+6}=8^{4x+5} ?

The answer to 2^{6x+3}x4^{3x+6}=8^{4x+5} is x=1

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2^{6x+3}x4^{3x+6}=8^{4x+5}

2^{6 x + 3} x 4^{3 x + 6} = 8^{4 x + 5}

x = 1

Solution steps

2^{6 x + 3} x \cdot 4^{3 x + 6} = 8^{4 x + 5}

Apply exponent rules

2^{6 x + 3 + 2 (3 x + 6)} x = (2^{3})^{4 x + 5}

Subtract

2^{3 (4 x + 5)}

from both sides

2^{6 x + 3 + 2 (3 x + 6)} x - 2^{3 (4 x + 5)} = 2^{3 (4 x + 5)} - 2^{3 (4 x + 5)}

Simplify

2^{6 x + 3 + 2 (3 x + 6)} x - 2^{3 (4 x + 5)} = 0

Factor

8^{5 + 4 x} (x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

8^{5 + 4 x} = 0 or x - 1 = 0

Solve

8^{5 + 4 x} = 0 :

No Solution for

x \in R

Solve

x - 1 = 0 : x = 1

x = 1

4^{x - 4} = 32

1. 5^{x} = 5.25

2^{4 b + 3} = 128

7^{2 x} - 48 (7^{x}) - 49 = 0

8 1^{x - 1} = 3^{8}

What is the answer to 2^{6x+3}x4^{3x+6}=8^{4x+5} ?
The answer to 2^{6x+3}x4^{3x+6}=8^{4x+5} is x=1
Solve for x: 2^{6x+3}x4^{3x+6}=8^{4x+5}
The solution is x=1