How do you solve for x?

Question

10^x = 357
Thanks

Answer 1

10^x = 357

So use logarithms:

log _base 10 (357) = x
log (357) = x

x = 2.552668216


PS...Anytime you have an exponent equaling something on the other side of the equal side you can do this. It's just the exponential version of log. Here's a basic formula:

y = log_base a (x)
a^y = x

Answer 2

Hey there!

Since the base in the left side of the equation, 10^x=357, is 10, it is better to use a common log rather than a natural log.

Remember that a common log is a base 10 log, whereas a natural log is a base e log.

Here's the answer.

10^x=357 --> Write the problem.
log(10^x)=log(357) --> Take the common log on each side of the equation.
x=log(357) --> Use the exponential-logarithmic inverse properties on the left side of the equation i.e. log(10^x)=x.
x≈2.553 Approximate the above answer to the nearest thousandth.

So the answer is x=log(357) or x≈2.553.

Hope it helps!

Answer 3

x = log 357

10^2 = 100 and 10^3 = 1000 so x is between 2 and 3.

2.5526682 is the value I got by referring to a table. Note that log 100 is 2 and log 3.57 = 0.5526682

Answer 4

lg (10^x) = lg 357
x lg10 = lg 357
x = (lg 357) / (lg 10)
(i dont have the calculator with me to work out the rest right now... Hope this helps)