# Algebra 2

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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.

• Algebra 2 -

on the right side you have

2log(base2)^10
or
2log210

there is no such notation.

The expression on the left is even worse.

• Algebra 2 -

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

• Algebra 2 -

In this and most forums the ^ is used as an exponent indicator
e.g. 2^3 = 23

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

log(base2)^(x-3)log(base2)^5 = 2log(base2)^10 is really
log(base2)(x-3)log(base2)5 = 2log(base2)10 or
log2(x-3)log25 = 2log2100
divide by log25
log2(x-3) = log2100/log25
log2(x-3) = log100/log5 = 2.861353
so x-3 = 2^2.861353
x-3 = 7.26697
x = 10.26697

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