Question

Find the value of:
i) $\log_{5} 3125$
ii) $\log_{7} \sqrt[3]{7}$

Answer 1

Hey dear,
You just need basic logarithsms knowledge for this.

● Important formula here -
$log_{a}(a) = 1$
$log_{a}( {b}^{m} ) \: = m \: log_{a}(b)$

● Solution -
1) $log_{5}(1325)$
$log_{5}(1325) = log_{5}( {5}^{5} )$
$log_{5}(1325) = 5 \: log_{5}5$
$log_{5}(1325) = 5$

2) $log_{7}( \sqrt[3]{7} )$
$log_{7}( \sqrt[3]{7} ) = \: log_{7}( {7}^{ \frac{1}{3} } )$
$log_{7}( \sqrt[3]{7} ) \: = \frac{1}{3} \: log_{7}( 7 ) \:$
$log_{7}( \sqrt[3]{7} ) \: = \frac{1}{3}$


Hope it helps...

Answer 2

Answer:

i) 4

ii) 1/3

Step-by-step explanation:

Hi,

If y = aˣ, then we define x as logₐy  (or)

If x = logₐy , then y = aˣ

Here , a > 0 and a ≠ 1 , a is called the base of the  

logarithm.

i) Let x = log₅3125

Using the definition of logarithm, we can rewrite in

exponential form as

5ˣ = 3125

We can write 3125 as 5⁵

So, 5ˣ = 5⁴

Since bases are equal, exponents should  be equal

Hence, x = 4.

ii) Let x = log₇∛7

Using the definition of logarithm, we can rewrite in

exponential form as

7ˣ = ∛7

We can write ∛7 as 7¹/³

So, 7ˣ = 7¹/³

Since, bases are equal, exponents should be equal

Hence, x = 1/3

Hope, it helps !