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25^x=3,125

I don't understand how to do this 

Posted in Math, asked by Jane , 6 years ago. 6952 hits.

3

The other answers are valid, but require you to spot that 3125=55 which is not always practical.

A quicker alternative (that will work equally well for less convenient numbers) is to use a logarithm: if bx=a then logba=x, so

log253125 = x = 2.5

or, if you can only calculate natural logs for whatever reason, 

x = log253125 = log(3125)/log(25) = ~3.495/~1.398 = 2.5

Russell Ludlow
Russell Ludlow - 6 years ago
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2

25^x=3125

we will take the L.C.M  of 3125 i.e. 5*5*5*5*5=5^5

(5^2)^X= 5^5

now  (a^m)^n=a^mn

we will put the problem in the given formula then

   5^2x=5^5

now, a^m=a^n =>m=n

according to formula, 2x=5

                             = x=5/2

 

 

Venkat Nagendra Thati
Venkat Nagendra Thati - 6 years ago
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2

25x = 3,125  ----> This is an exponential equation (How can you get the value of x?)

 

52(x) = 55     -----> For this equation, the base is 5 and the exponents for 25 and 3,125 are 2 and 5   respectively.

 

2x = 5        ----->  remove the base 5, and the value of x is:

 

x = 5/2

 

Reynan Flores
Reynan Flores - 6 years ago
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1

25^x = ((5)^2)^x = 5^2x

3125 = ((25)^2) * 5 = 5^5

equating two above equations we get

2x= 5

x = 5/2 = 2.5

Vritika Gupta
Vritika Gupta - 6 years ago
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