Question

Find the logarithm of : 27 to the base 9

Answer 1

The answer is 2/3 .

Method 1

log27(9)

can be interpreted as " 27 to what power is equal 3=32=9,log27(9)=2/3 .

Method 2

If it is difficult to see directly, another technique is to change the base:

log27(9)

can be rewritten as

log3(9)log3(27)=2/3

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Answer 2

${\huge{\bold{\purple{\bigstar{\boxed{\boxed{\bf{Question}}}}}}}}$

Find the logarithm of : $log27_9$

${\huge{\bold{\purple{\bigstar{\boxed{\boxed{\bf{Solution}}}}}}}}$

$\sf\implies log 27_9 = x$

$\sf\implies 27=9^x$

$\sf\implies3^3=3^{2x}$

• bases are equal therefore power will also be equal

$\sf\implies x=\dfrac{3}{2}$

${\bold{\blue{\boxed{\bf{\dag x = \dfrac{3}{2} }}}}}$

${\huge{\bold{\green{\bigstar{\boxed{\boxed{\bf{Extra\: info:-}}}}}}}}$

• A logarithm is the power to which a number must be raised in order to get some other number
• Logarithms are a way of showing how big a number is in terms of how many times you have to multiply a certain number to get it.