The solution of 642x-5-4-8x-5 is

Applying the law of exponents and solving the equations:64^2x 5=4×8^x 50ex0ex2^6(2x 5)=2^2×2^3(x 5)0ex0ex2^12x 30=2^3(x 5)+20ex0ex2^12x 30=2^3x 15+20ex0ex2^12x ...

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Standard XII

Mathematics

Standard Formulae - 3

The solution ...

Question

The solution of $64^{2 x - 5} = 4 \times 8^{x - 5}$ is

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Solution

Applying the law of exponents and solving the equations:
$64^{2 x - 5} = 4 \times 8^{x - 5} 2^{6 (2 x - 5)} = 2^{2} \times 2^{3 (x - 5)} 2^{12 x - 30} = 2^{3 (x - 5) + 2} 2^{12 x - 30} = 2^{3 x - 15 + 2} 2^{12 x - 30} = 2^{3 x - 13}$
Now comparing the bases of $2$ .
$\begin{array}{rcl} 12 x - 30 & = & 3 x - 13 \\ 12 x - 3 x & = & 30 - 13 \\ 9 x & = & 17 \\ x & = & \frac{17}{9} \end{array}$
Hence, the solution of the equation is $\begin{array}{rcl} \frac{17}{9} \end{array}$ .

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Question 53

State whether the statement is True or False.

$\frac{3}{2}$ is the solution of the equation 8x - 5 = 7.

Q. The solution of

64^{2 x - 5} = 4 \times 8^{x - 5}

Look at the pattern and fill in the blanks:

$5 = 4 \times 1 + 1$ , For $1^{st}$ term or $n = 1$

$9 = 4 \times 2 + 1$ , For $2^{nd}$ term or $n = 2$

$13 = 4 \times 3 + 1$ , For $3^{rd}$ term or $n = 3$

$17 = 4 \times 4 + 1$ , For $4^{th}$ term or $n = 4$

$21 = 4 \times 5 + 1$ , For $5^{th}$ term or $n = 5$

$∴$ Expression for $n^{th}$ term is $4 n + 1$ .

(i) For $n = 8$ , $4 \times____+ 1 =____$ .

Q. Identify the solution set for

\frac{7 x - 5}{8 x + 3} > 4

Q. Number of positive integral solution of the

| x | | x - 5 | + | 24 - 3 x | = | x^{2} - 8 x + 24 |

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The solution of 642x−5=4×8x−5 is

Applying the law of exponents and solving the equations:642x−5=4×8x−526(2x−5)=22×23(x−5)212x−30=23(x−5)+2212x−30=23x−15+2212x−30=23x−13Now comparing the bases of 2.12x-30=3x-1312x-3x=30-139x=17x=179Hence, the solution of the equation is 179.

The solution of $64^{2 x - 5} = 4 \times 8^{x - 5}$ is