How do you solve 2x5=10x?

2 Answers
Jun 30, 2016

If A=B, then logA=logB:

log(2x×5)=log(10x)

Use the rule loga(nm)=loganlogam to simplify.

log2x+log5=log10x

Use the rule logan=nloga to simplify further.

xlog2+log5=xlog10

log5=xlog10xlog2

Factor out the x.

log5=x(log10log2)

Put back the logs on the left side into quotient form to simplify.

log5=x(log(102))

log5=x(log5)

Isolate x.

log5log5=x

1=x

Checking in the original equation, we find that this solution works.

Hopefully this helps!

Jun 30, 2016

x=1 (using alternate solution method)

Explanation:

If 2x5=10x

2x5=(25)x

2x5=2x5x

5=5x

x=1