Question

find a if 2^a-3 * 5^2a-5= 250

Answer 1

Hello Dear Brainly user...

Solution for your

Question

Given that:-

2 ^ (a -3) × 5 ^ (2a -5) = 250

we know that;

Log m× n = log m + log n

and

Log m ^n = n × log m

Now,

Taking log on both side

Log { 2 ^ (a -3) × 5 ^ (2a -5) } = log 250

=> log 2 ^ (a -3) + log 5 ^ (2a -5) = log( 125 × 2)

=> (a -3) × log 2 + (2a -5) × log 5 = log (5³ × 2)

=>(a -3) × log 2 + (2a -5) × log 5 = log 5³ + log 2

=> a log2 - 3 log2 + 2a log5 - 5 log5 = 3 log 5 + log 2

=> By shifting...

=> a [ log 2 + 2 log5 ] = 3 log5 + log 2 + 3 log2 + 5 log5

=> a [ log 2 + 2 log 5] = 8 log 5 + 4 log 2

=> a [ log 2 + 2 log 5] = 4 { 2 log 5 + log 2}

By comparing...

=> a = 4 Answer

Hope it helps...

:-)