Posted by **Ana** on Sunday, February 28, 2010 at 8:31pm.

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 -
**Reiny**, Sunday, February 28, 2010 at 10:50pm
your notation makes no sense

on the right side you have

2log(base2)^10

or

2log_{2}^{10}

there is no such notation.

The expression on the left is even worse.

- Algebra 2 -
**Ana**, Sunday, February 28, 2010 at 10:57pm
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 -
**Reiny**, Sunday, February 28, 2010 at 11:17pm
In this and most forums the ^ is used as an exponent indicator

e.g. 2^3 = 2^{3}

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_{2}(x-3)log_{2}5 = 2log_{2}100

divide by log_{2}5

log_{2}(x-3) = log_{2}100/log_{2}5

log_{2}(x-3) = log100/log5 = 2.861353

so x-3 = 2^2.861353

x-3 = 7.26697

x = 10.26697

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