<PRE><B>Question 1130719</B>
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Although the solution by tutor @ikleyn is probably correct for the INTENDED problem, it has nothing to do with the problem as presented.&lt;br&gt;
In the expression &quot;10^4logx&quot; there are two operations -- an exponentiation and a multiplication.  In standard order of operations, exponentiation is done first.  So the equation as you show it is&lt;br&gt;
{{{10^4logx - 7(10^2logx) + 10 = 0}}}&lt;br&gt;
To solve this equation....&lt;br&gt;
{{{10000logx-700logx = -10}}}
{{{9300logx = -10}}}
{{{logx = -10/9300 = -1/930}}}
{{{x = 10^(-1/930)}}}&lt;br&gt;
which to 6 decimal places is 0.997527.&lt;br&gt;
The intended equation is almost certainly&lt;br&gt;
{{{10^(4logx) - 7(10^(2logx)) + 10 = 0}}}&lt;br&gt;
Please be polite when you post questions: use parentheses where required so we don&#39;t need to guess what the real question is.&lt;br&gt;
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I have to respond to the absurd comments tutor @MathTherapy made about my response....&lt;br&gt;
In my response, I acknowledged that the PROBABLE intent of the problem was with the equation&lt;br&gt;
{{{10^(4logx) - 7(10^(2logx)) + 10 = 0}}}&lt;br&gt;
But I also pointed out that, as the problem is presented, it is something very different, with a very different solution.&lt;br&gt;
And my response included a statement, intended for the person who submitted the problem, showing that the use of parentheses was important.  That was a useful thing to include.&lt;br&gt;
Tutor @MathTherapy&#39;s remarks about my response:&lt;br&gt;
&quot;He doesn&#39;t have much sense and just loves to criticize.&lt;br&gt;
Plus, he thinks he knows everything.&quot;&lt;br&gt;
My comments to his comments....&lt;br&gt;
(1) I have enough sense to know for a fact that exponentiation has precedence over multiplication, and therefore the correct solution to the problem as presented is what I showed.  Perhaps he doesn&#39;t know that....&lt;br&gt;
(2) There is nothing about my response that can be characterized as a criticism.  I presented an informative response that was intended to show that the use of parentheses is important.&lt;br&gt;
As for loving to criticize, his answer is nothing but a criticism, along with a repetition of a solution already provided by another tutor.&lt;br&gt;
Take a look at the answers he has provided in this forum and see how often his response is nothing but a criticism of another tutor, sometimes accompanied by an answer with no work shown, which doesn&#39;t help the reader learn anything.&lt;br&gt;
Then decide for yourself who it is that loves to criticize.
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