Algebra HW Question

Question

Log (1/100,000,000) = -8.

The equation in exponential form is:

Answer 1

10^-8 = 1/100,000,000 = 1/10^8 = 10^-8

10^-8 = 1 x 10^-8 in scientific notation

this assumes Log(1/100,000,000) is log to the base 10, the common log

the 10 is implicit

but in higher math, "log" often refers to the natural log, "ln," to base e,

an implicit base e rather than an implicit 10 for "log."

You can comvert a log in any base to a log in any other base

log_ba = x

x = lna/lnb

lna = xlnb

for b= 10 and a = 10^-8, x = 10^-8

lna = ln(10^-8) = xlog_e10 = 10^-8(2.3026) = about 2.3026/100,000,000 == 23026 x 10^-12 = about 2.3 x 10^-8

or use Desmos' change of base calculator,