136k views
0 votes
−7⋅30.25x=−10 Solve exponential equations using logarithms: base-2 and other bases

User Tomoe
by
8.4k points

1 Answer

4 votes

Answer:

x = 0.1046

Explanation:

I have chosen to interpret your −7⋅30.25x=−10 as being:

-7(30.25)^x = -10 and have the goal of solving this for x. Note that this problem, interpreted in this way, does not involve base 2.

Starting with −7⋅30.25^x=−10, divide both sides by -7. The result is:

30.25^x = 10/7

Taking the log (to the base 10) of both sides, we get:

x log 30.25 = log 10 - log 7 = 1 - log 7

1 - log 7 0.1549

Then x = ---------------- = --------------- = 0.1046

log 30.25 1.4807

x = 0.1046

If this is not the answer you expected, please double check to ensure that you have copied down the problem correctly.

User Paul Spaulding
by
7.8k points