Question

If (2raised to the power 3x-1 plus 10) ÷7=6, then x is equal to?


please solve this question...step by step...fasttt

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Answer 1

★ Given :

$\left(2^{3x-1} + 10\right) \div 7 = 6$

★ To find:

the value of x

★ Solution:

$\frac{(2^{3x-1} + 10)}{7} = 6$

$by \:cross \: multiplication \\ \\ \\ 2^{3x-1} + 10 = 6 \times 7 \\ \\ \\ 2^{3x-1} + 10 = 42 \\ \\ \\ 2^{3x-1} = 42 - 10 \\ \\ \\ 2^{3x-1} = 32 \\ \\ \\ 32 = 2^5 \\ \\ \\ 2^{3x-1} = 2^5 \\ \\ \\ powers\: become \: equal \: when\: base \: is \: equal \\ \\ \\ 3x - 1 = 5 \\ \\ \\ 3x = 5+1 \\ \\ \\ 3x = 6 \\ \\ \\ x = \frac{\cancel{6}}{\cancel{3}} \\ \\ \\ {\pink{\boxed{x = 2}}}$

★ Verification :

$by \: putting \: value \: of \: x \\ \\ \\ \frac{(2^{3(2)- 1} + 10)}{7} = 6 \\ \\ \\ \frac{2^5 + 10}{7} = 6 \\ \\ \\ \frac{32+10}{7} = 6 \\ \\ \\ \frac{42}{7} = 6 \\ \\ \\ 6 = 6 \\ \\ \\ \purple{LHS = RHS} \\ \\ \\ \sf\blue{Hence \: verified}$