How do you solve 2^x*5=10^x?

2 Answers
Jun 30, 2016

If A = B, then logA = logB:

log(2^x xx 5) = log(10^x)

Use the rule log_a(n/m) = log_an - log_am to simplify.

log2^x + log5 = log10^x

Use the rule loga^n = nloga to simplify further.

xlog2 + log5 = xlog10

log5 = xlog10 - xlog2

Factor out the x.

log5 = x(log10 - log2)

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

log5 = x(log(10/2))

log5 = x(log5)

Isolate x.

log5/log5 = 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 2^x*5=10^x

rArr 2^x*5 =(2*5)^x

rArr 2^x*5 = 2^x*5^x

rArr 5=5^x

rArr x=1