Question

Solve the following equation.

1). 3+2^x = 64^1/2+27^1/3


2). 2^x = (128)^1/7 × (√2)^4​

Answer 1

Answer:

1) 3

2) 3

Step-by-step explanation:

Answer 2

Answers:

1)

$3+2^{x}= 64^{\frac{1}{2} } + 27^{\frac{1}{3}}$

$3+2^{x}= \sqrt{64} + \sqrt[3]{27}$

$3+2^{x}= 8 + 3$

$2^{x}= 8 + 3 - 3$

$2^{x}= 8$

$2^{x}= 2^{3}$

$x = 3$

∴ x = 3

2)

$2^{x} = 128^{\frac{1}{7}} \times (\sqrt{2})^{4}$

$2^{x} = (2^{7}) ^{\frac{1}{7}} \times (2^{\frac{1}{2}} )^{4}$

$2^{x} = 2^{1} \times 2^{2}$

$2^{x} = 2^{1 + 2}$

$2^{x} = 2^{3}$

$x = 3$

∴ x = 3