What is 0.514 written as a power of 10?

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Answer 1 · 2018-05-10T13:28:24

Approximate answer #->x~~-0.2890 # to 4 decimal places

Exact answer #color(white)("ddddd.")-> x=ln(0.514)/ln(10)#

#10^((ln(0.514))/(ln(10)))=0.514#

Let the unknown value be #x#

Set #10^x=0.514#

Take logs of both sides. I choose # log_e ->ln#

#ln(10^x)=ln(0.515)#

But the general case of #ln(a^b)=bln(a)#. So using this principle we have:

#xln(10)=ln(0.514)#

Divide both sides bu #ln(10)#

#x=ln(0.514)/ln(10)~~ -0.28903688....#

#x~~-0.2890# to 4 decimal places