Question

if (4)^-3 *(4)^2x =(4)^5 find the value of x

Answer 1

Answer:

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Class 11

>>Applied Mathematics

>>Logarithm and Antilogarithm

>>Indices

>>If 2^x × 4^x = (8)^1/3 × (32)^1/5 the

Question

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If 2

x

×4

x

=(8)

3

1

×(32)

5

1

then, find the value of x

Easy

Solution

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We have,

2

x

×4

x

=(8)

3

1

×(32)

5

1

2

x

×(2

2

)

x

=((2

3

))

3

1

×(2

5

)

5

1

2

x

×2

2x

=2×2

2

x+2x

=2

2

2

3x

=2

2

On comparing both sides, we get

3x=2

x=

3

2

Hence, this is the answer.

Answer 2

Answer:

x=4

Explanation:-

${ 4}^{ - 3} \times {4}^{2x} = {4}^{5} \\ {4}^{2x + ( - 3)} = {4}^{5} \\ exponent \: equation \\ \\ 2x - 3 = 5 \\ 2x = 5 + 3 = 8 \\ 2x = 8 \\ x = \frac{8}{2} = 4 \\ x = 4$