Question

If log of x to the base 9 + log of x to the base 3 =3/2 then X is​

Answer 1

In logarithm we will practice different types of questions on how to solve logarithmic functions on log. Solved examples on logarithm will help us to understand each and every log rules and their applications. Solving logarithmic equation are explained here in details so that student can understand where it is necessary to use logarithm properties like product rule, quotient rule, power rule and base change rule.

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Step-by-step solved example in Log:

1. Find the logarithms of:

(i) 1728 to the base 2√3

Answer 2

x = 3

Step-by-step explanation:

Given: $log_9x+\log_3x=\dfrac{3}{2}$

Using base change property of log:

$\log_ab=\dfrac{\log b}{\log a}$

$\dfrac{\log x}{\log 9}+\dfrac{\log x}{\log 3}=\dfrac{3}{2}$

using property of exponent:

$\log a^m=m\log a$

$\dfrac{\log x}{2\log 3}+\dfrac{\log x}{\log 3}=\dfrac{3}{2}$

make same denominator

$\dfrac{\log x+2\log x}{2\log 3}=\dfrac{3}{2}$

using addition property of log:$\log a+\log b = \log ab$

$\dfrac{\log x^3}{2\log 3}=\dfrac{3}{2}$

$\log x^3=\log 3^3$

$x^3=3^3$

$x=3$

Hence, the value of x is 3

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