# How to solve a following algebraic equation preferably with a calculator or algebraically?

The question is $$1000=800(1+.0175/12)^{12x}$$ the 12 x is the exponent, i would like if some one could help me find the following with the help of the calculator but if there is a way you can solve algebraically as when i entered 1000 in the calculator's y2, i could not see them intersect?

i plugged the 1000 in y 2 and the above equation on y1, but for some reason the intersection between those two were wrong , i than plugged the problem on desmos online calculator and got the right answer? what could be wrong as when i was trying to find the intersection i got something like (1.3, 1000) but the asnwer is 12.76,1000

• hint: put down the graphing calculator and graph it by hand with a pencil and some graph paper. To find values, calculate $(1+0.0175/12)^{12}$, store it with the M+ button, then take 800 and repeatedly multiply it by the value in the memory location (MR button). You should find that the tally exceeds 1000 when you press the equals sign for the 13th time, corresponding to $12\lt x\lt 13$. – John Joy Nov 6 '15 at 0:49

algebraically, you can divide both sides by $800$, then take the logarithm of both sides. which would give:
$$\log\frac{5}{4}=12x\log(1+0.175/12)$$
Then evaluate the log on the right side (call this result $\alpha$). Then divide both sides by $12\alpha$
• The graphs do intersect at around $x = 12.76$, as you can see here: wolframalpha.com/input/… It might be that your calculator is not strong enough or the window is looking at the wrong part of the graph. – Denwid Nov 5 '15 at 22:54
• hmm..well when i did just graph the equation $$y = 800(1+.0175/12)^{12x}$$ , the Y value was up in the 40000? – MATH ASKER Nov 5 '15 at 22:59
• The solution is simply $$\frac{\log\frac54}{12\log(1+\frac{0.175}{12})}.$$ Any calculator should be able to calculate this number. – 5xum Nov 6 '15 at 1:24