Find the value of 'p':
3 raised to the power (3p-4) - 5 raised to the power (2p-1) =1125
 

Asked by Chhavi | 14th May, 2016, 05:02: PM

Expert Answer:

C o n s i d e r space t h e space g i v e n space e q u a t i o n colon 3 to the power of open parentheses 3 p minus 4 close parentheses end exponent minus 5 to the power of open parentheses 2 p minus 1 close parentheses end exponent equals 1125 N o w space c o n s i d e r space t h e space p o w e r s space o f space 3 3 to the power of 0 equals 1 3 to the power of 1 equals 3 3 squared equals 9 3 cubed equals 27 3 to the power of 4 equals 81 3 to the power of 5 equals 243 3 to the power of 6 equals 729 3 to the power of 7 equals 2187 . . . . O b s e r v e space t h e space u n i t space d i g i t s space o f space p o w e r s space o f space 3. T h e y space a r e space 1 comma 3 comma 9 space a n d space 7 space a n d space t h e y space r e c u r space s u b s e q u e n t l y. T h u s comma space i t space i s space c l e a r space t h a t space i t space w i l l space n e v e r space e n d space w i t h space t h e space u n i t space d i g i t space 0 T h e space s u b t r a h e n d space i s space g i v e n space a s space 5 to the power of open parentheses 2 p minus 1 close parentheses end exponent T h e space p o w e r s space o f space 5 space a r e colon 5 to the power of 0 equals 1 5 to the power of 1 equals 5 5 squared equals 25 5 cubed equals 125 5 to the power of 4 equals 625 5 to the power of 5 equals 3125 . . . O b s e r v e space t h e space u n i t space d i g i t s space o f space p o w e r s space o f space 5 T h e y space a l w a y s space e n d space w i t h space 5 space e x c e p t space f o r space 5 to the power of 0. T h e space u n i t space d i g i t space i n space t h e space a n s w e r space i s space 5 T h u s space t h e space u n i t space d i g i t space o f space t h e space m i n u e n d comma space t h a t space i s space 3 to the power of open parentheses 3 p minus 4 close parentheses end exponent space s h o u l d space b e space 0 space t o space g e t space 5 space a s space t h e space u n i t space d i g i t space i n space t h e space a n s w e r. B u t space h e r e space sin c e space t h e space u n i t space d i g i t space o f space t h e space m i n u e n d comma space t h a t space i s space 3 to the power of open parentheses 3 p minus 4 close parentheses end exponent space i s space n o t space z e r o comma space t h i s space i s space n o t space p o s s i b l e. H e n c e space t h e r e space i s space s o m e space e r r o r space i n space t h e space q u e s t i o n. P l e a s e space c h e c k space t h e space q u e s t i o n.

Answered by Vimala | 16th May, 2016, 09:45: AM

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