i cant solve this problem please help me to solve

Question

find the value of log_0.6(9/25)

Answer 1

Hi Sheeba,

 

We can use the "change of base" rule (going from any base to base 10), which says:

    log_a(b) = log(b) / log(a)

 

Applying this rule to our problem

(going from base 0.6 to base 10):

    9/25 = (4/4)(9/25) = 36/100 = 0.36

    log_o.6(0.36) = log(0.36) / log(0.6) = 2

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.

Answer 2

Let x = log_0.6(9/25)

 

x = log_(6/10)(9/25)

 

 

The solution to a logarithm is the exponent of its base.  The base is 6/10.

 

(6/10)^x = 9/25

 

(3/5)^x = 9/25

 

 

According to the rules of exponents, we can rewrite the equation as

 

3^x / 5^x = 9 / 25

 

3² / 5² = 9 / 25

 

(3 / 5)² = 9 / 25

 

x = 2

 

 

Therefore,

 

log_0.6(9/25) = 2

 

 

 

Answer 3

let log(0.6)(9/25)=x

therefore (0.6)^x=(9/25)

(0.6)^x=(3/5)^2

0.6=6/10=3/5

(3/5)^x=(3/5)^2

if the bases are equal then the exponents must be equal

x=2 so log(0.6)(9/25)=2

or,...

log(0.6)(9/25)=log(0.6)(3/5)^2=log(0.6)(0.6)^2=2log(0.6)(0.6)=2*1=2 again