Question

If
$(2 ^{3x - 1} + 10) \div 7 = 6$
then x is equal to
(a) -2
(b) 0
(c) 1
(d) 2​

Answer 1

$2 ^{3x - 1} + 10 = 42 \\ {2}^{3x - 1} = 32 \\ 2 {}^{3x - 1} = {2}^{5 } \\ comparing \: the \: powers \\ 3x - 1 = 5 \\ 3x = 6 \\ x = 2$

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Answer 2

Given,

$\longrightarrow\sf{\dfrac {2^{3x - 1} + 10}{7}= 6}$

Multiplying both sides by 7,

$\longrightarrow\sf{2^{3x - 1} + 10= 42}$

Now subtract 10 from both sides. We get,

$\longrightarrow\sf{2^{3x - 1}= 32}$

Taking logarithm to the base 2,

$\longrightarrow\sf{\log_232= 3x-1}$

But $\sf{\log_232=5.}$ Then,

$\longrightarrow\sf{3x-1=5}$

Finally,

$\longrightarrow\sf{\underline {\underline {x=2}}}$