Question

4to the power (x+2)+ 2to the power (2x+3)= 96
​

Answer 1

Answer:

x = 1

Step-by-step explanation:

$4^{x+2} + 2^{2x+3} = 96$

$4^{x}.4^{2} + 2^{2x}.2^{3} = 96$

$2^{2x}.16 + 2^{2x}.8 = 96$

$2^{2x}(16 + 8) = 96$

$2^{2x} = \frac{96}{24}$

$2^{2x} = 4$

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

Comparing same bases,

2x = 2

x = 1

Answer 2

Answer:

x=1

Step-by-step explanation:

964

x+2

+2

2x+3

=96

4^{x}.4^{2} + 2^{2x}.2^{3} = 964

x

.4

2

+2

2x

.2

3

=96

2^{2x}.16 + 2^{2x}.8 = 962

2x

.16+2

2x

.8=96

2^{2x}(16 + 8) = 962

2x

(16+8)=96

2^{2x} = \frac{96}{24}2

2x

=

24

96

2^{2x} = 42

2x

=4

2^{2x} = 2^{2}2

2x

=2

2

Comparing same bases,

2x = 2

x = 1