Exponential equations reducible to quadratics (1 Viewer)

[mdm92]

If anyone could answer this question it would be much appreciated.

5^2x-26.5^x+25=0

Thanks

 

[untouchablecuz]

If anyone could answer this question it would be much appreciated.

5^2x-26.5^x+25=0

Thanks

5^2x-26.5^x+25=(5^x)^2-26(5^x)+25

let u=5^x

u^2-26u+25=0

(u-25)(u-1)=0

u=25 or u=1

but u=5^x

.'. 5^x=25=5^5 --> x=5

and 5^x=1=5^0 --> x=0

 

[khorne]

5^2x-26.5^x+25=(5^x)^2-26(5^x)+25

let u=5^x

u^2-26u+25=0

(u-25)(u-1)=0

u=25 or u=1

but u=5^x

.'. 5^x=25=5^5 --> x=5

and 5^x=1=5^0 --> x=0

5^x = 25...x = 2