Algebra , Exponents

Algebra Level 1

If 64 2 x − 5 = 4 × 8 x − 5 { 64 }^{ 2x-5 }=4\times { 8 }^{ x-5 } then the value of x x is

17 9 \frac { 17 }{ 9 } 20 9 \frac { 20 }{ 9 } 9 17 \frac { 9 }{ 17 } 17 10 \frac { 17 }{ 10 }

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Ankit Vijay by Ankit Vijay , 22, India

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3 solutions

Micah Wood
Jun 17, 2014

6 4 2 x − 5 = 4 × 8 x − 5 ( 2 6 ) 2 x − 5 = 2 2 × ( 2 3 ) x − 5 2 6 ( 2 x − 5 ) = 2 2 + 3 ( x − 5 ) 6 ( 2 x − 5 ) = 2 + 3 ( x − 5 ) 12 x − 30 = 3 x − 13 9 x = 17 x = 17 9 \large 64^{2x-5} = 4\times 8^{x-5} \\ \large (2^6)^{2x-5} = 2^2\times(2^3)^{x-5} \\ \large 2^{6(2x-5)} = 2^{2+3(x-5)} \\ \large 6(2x-5) = 2+3(x-5) \\ \large 12x-30 = 3x-13 \\ \large 9x = 17 \\ \large\boxed{x = \dfrac{17}{9}}

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Ankit Vijay
Jun 2, 2014

64 2 x − 5 = 4 × 8 x − 5 = 64 2 x − 5 8 x − 5 = 4 = 8 3 x − 5 = 4 = 2 9 x − 15 = 2 2 = 9 x = 17 x = 17 9 { 64 }^{ 2x-5 }=4\times { 8 }^{ x-5 }\\ \\ \\ =\frac { { 64 }^{ 2x-5 } }{ { 8 }^{ x-5 } } =4\\ \\ \\ { =8 }^{ 3x-5 }=4\\ \\ \\ =2^{ 9x-15 }={ 2 }^{ 2 }\\ \\ \\ =9x=17\\ \\ \\ x=\frac { 17 }{ 9 }

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vijay i have problem in one qs i write it in posting box but cant posted why

Zubair Afridi - 6 years, 11 months ago

qs is(4+15^1/2)^x+(4-15^1/2)^x=62 then x=?

Zubair Afridi - 6 years, 11 months ago

8^3x-5 how it come

Zubair Afridi - 6 years, 11 months ago
William Isoroku
Aug 2, 2014

Just put everything into base 2.

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