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Nick88888888
 one year ago
(1.05)^x = 2.5
Round your answer to the nearest tenth. how would i do this step by step?
2.
___
√ 3x = 50 Round your answer to the nearest tenth.
Nick88888888
 one year ago
(1.05)^x = 2.5 Round your answer to the nearest tenth. how would i do this step by step? 2. ___ √ 3x = 50 Round your answer to the nearest tenth.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Apply logarithm of base 10 to both the sides \[\log_{10}((1.05)^{x})=\log_{10}(2.5)\] Rule: 1.\[\log(x^y)=y.\log(x)\] (true for all base) 2.\[\log_{a}a=1\] log of any number to it's base is 1 3.\[\log(a \times b)=\log(a)+\log(b)\] 4.\[\log(\frac{a}{b})=\log(a)\log(b)\] Also true for all base 5.\[\log(1)=0\] Also true for all base \[x.\log_{10}(1.05)=\log_{10}(\frac{10}{4})\] Here's the first I've applied property 1 to left side and written right side 2.5 as 10/4 use property 4 on right side now Note on the right side I've written 2.5 as 10/4

Nick88888888
 one year ago
Best ResponseYou've already chosen the best response.0Ok so i just do (1.05)(10/4) or... what

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Do you know about logarithms?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok Consider an example \[(0.4)^x=\frac{0.25}{100}\] Apply log of base 10 to both sides \[\log_{10}(0.4)^x=\log_{10}(\frac{0.25}{100})\] Use rule 1 on left side and rule 4 on right side \[x.\log_{10}(0.4)=\log_{10}(0.25)\log_{10}(100)\] Now we can write 0.4 as 4/10 0.25 as square of 0.5 and 100 as square of 10 so do that \[x.\log_{10}(\frac{4}{10})=\log_{10}((0.5)^2)\log_{10}(10^2)\] Property 4 on left and property property 1 on right \[x[\log_{10}(4)\log_{10}(10)]=2\log_{10}(0.5)2\log_{10}(10)\] We can write 4 as 2 square and 0.5 as 1/2 so do that \[x[\log_{10}(2^2)\log_{10}(10)]=2[\log_{10}(\frac{1}{2})\log_{10}(10)]\] Use properties to simplify further \[x[2\log_{10}(2)\log_{10}(10)]=2[\log_{10}(1)\log_{10}(2)\log_{10}(10)]\] Now put the values in, \[\log_{10}(2)=0.3010\] By property 2 and property 5 the other values are \[\log_{10}(10)=1\]\[\log_{10}(1)=0\]\[x[2 \times 0.30101]=2[00.30101]\]\[0.398x=2.06\]\[x=\frac{2.06}{0.398}\approx 5.176\]

Nick88888888
 one year ago
Best ResponseYou've already chosen the best response.0sorry didnt mean to bump
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