Question

Please do in copy amswer is 3​

Answer 1

GIVEN :

$\mapsto \sf log_{10}(3x - 1) = 3 log_{10}2$

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SOLUTION :

$\sf \: \: \: \: \: \: \: \: \: \: \: \: log_{10}(3x - 1) = </u><u>3</u><u> log_{10}(2)$

$\sf \implies \: (3x - 1) = </u><u>8</u><u>$

$\sf \implies \: \: { \underline{\boxed { \sf{ x = </u><u>3</u><u>}}}}$

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LEARN MORE :

$\sf1) \: \: \: log_{a}1 = 0$

$\sf \: 2) {a}^{ log_{a}(x) } = x$

$\sf \: 3) log_{a}(xy) = log_{a}(x) + log_{a}(y)$

$\sf \: 4) \: log_{a}( \frac{x}{y} ) = log_{a}(x) - log_{a}(y)$

$\sf \: 5) log_{a}( {x}^{n} ) = n log_{a}(x)$

$\sf \: 6) \: log_{a}(b) = \frac{ log_{c}(b) }{ log_{c}(a) }$

$\sf7) \sf \: log_{a}(x) > 0 \: \: [ x\in {R}^{ + } ]$

$8) \sf base \: of \: log \: \not = 1 \: and \: > 0$

HAVE A WONDERFUL DAY

Answer 2

Question:-

$\mapsto$ Solve the equation and find the value of x.

Answer:-

$\mapsto$ The value of x is 3.

Step By Step Solution:-

Given,

$\sf \log_{10}(3x - 1) = 3 \log_{10}2$

$\sf \implies\log_{10}(3x - 1) = \log_{10}( {2}^{3} )$

$\sf \implies\log_{10}(3x - 1) = \log_{10}( 8 )$

Removing log from both sides,we get,

$\sf \implies 3x - 1 = 8$

$\sf \implies 3x = 8 + 1$

$\sf \implies 3x =9$

$\sf \implies x =3$

Hence, the value of x is 3 which is the required answer.

Formulae Used:-

1. $\sf \log(x) = \log(y) \implies x = y$
2. $\sf x \log(y) = \log( {y}^{x} )$

More Forumulae:-

1. $\sf \log(x) + \log(y) + ... = \log(xy...)$
2. $\sf \log( {x}^{y} ) = y \log(x)$
3. $\sf \frac{ \log(x)}{ \log(y)} = \log_{x}(y)$