How do I solve for x? Where I have 90=145+20log(50/x)

Question

889 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-09-19T09:46:24

# x = 2509.362 # (3dp)

or an exact answer

# x = 50 xx 10^2.7 #,

Assuming base #10# logarithms.

We have:

# 90=145+20log(50/x) #

Which can be rearranged step by step as follows:

# 145+20log(50/x) = 90#
# :. 20log(50/x) = 90-145#
# :. 20log(50/x) = -54#
# :. log(50/x) = -54/20#
# :. log(50/x) = -2.7#

Then, assuming base #10# logarithms:

# \ \ \ \ \ 50/x = 10^-2.7#

# :. x/50 = 10^2.7 #

# :. x = 50 xx 10^2.7#
# :. x = 2509.3618 ...#