Asked by Ana

solve the equation:
log(base2)^(x-3)log(base2)^5 = 2log(base2)^10

I don't know how to solve it, can someone help me? Please and thank you.
Answered by Reiny
your notation makes no sense
on the right side you have

2log(base2)^10
or
2log<sub>2</sub><sup>10</sup>

there is no such notation.

The expression on the left is even worse.
Answered by Ana
this is exactly what my homework sheet says. this is not teacher made, it's from the book. 2log(base2)^10 = log(base2)^10^2 = log(base2)^100
Answered by Reiny
In this and most forums the ^ is used as an exponent indicator
e.g. 2^3 = 2<sup>3</sup>

looking at your last line in the previous reply, I will assume that by
2log(base2)^10 = log(base2)^10^2 = log(base2)^100 you really meant :
2log(base2)10 = log(base2)10^2 = log(base2)100

so your question of
log(base2)^(x-3)log(base2)^5 = 2log(base2)^10 is really
log(base2)(x-3)log(base2)5 = 2log(base2)10 or
log<sub>2</sub>(x-3)log<sub>2</sub>5 = 2log<sub>2</sub>100
divide by log<sub>2</sub>5
log<sub>2</sub>(x-3) = log<sub>2</sub>100/log<sub>2</sub>5
log<sub>2</sub>(x-3) = log100/log5 = 2.861353
so x-3 = 2^2.861353
x-3 = 7.26697
x = 10.26697
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