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How would I solve something like 10^x = 6? watch

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    Hi .

    Can this be done without a calculator?

    What steps could I do to solve this or a question of this type?

    Thanks
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    X= log(10)6
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    (Original post by marcus888)
    Hi .

    Can this be done without a calculator?

    What steps could I do to solve this or a question of this type?

    Thanks
    You can use logs and leave it in exact form.

    So if you take logs of both sides (in base 10), you get log10^x=log6 and then you can use the log law that loga^n=n(loga) - you can write x(log10)=log6. Finally it's just simple division, divide both sides by log10 and you get x=log6/log10.

    And because log10=1 your answer is x=log6.
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    You'll definitely need a calculator.

    10^x=6 \iff log_{10} \left(10^x\right)=log_{10} 6 \iff x=log_{10} 6
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    (Original post by otah007)
    You'll definitely need a calculator.

    10^x=6 \iff log_{10} \left(10^x\right)=log_{10} 6 \iff x=log_{10} 6
    Which bit requires the use of a calculator, unless the question specifies to write the answer to some rounded figure?
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    (Original post by jamestg)
    Which bit requires the use of a calculator, unless the question specifies to write the answer to some rounded figure?
    I was assuming it needed a numerical value, if it needs an exact value then no calculator is needed.
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    (Original post by marcus888)
    Hi .

    Can this be done without a calculator?

    What steps could I do to solve this or a question of this type?

    Thanks
    The step can be solved without a calculator indeed. As the variable x is a power, you have to form the logarithm of this term (see otah007s step in comment #4)

    To get the concrete value of x, I would recommend you to use a calculator, otherwise you have to calculate a lot by approximating the value step by step.
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    (Original post by marcus888)
    Hi .

    Can this be done without a calculator?

    What steps could I do to solve this or a question of this type?

    Thanks
    Hi,

    The opposite of the "10^x" function is the log function (log to base 10 = "log" on calculator).

    You'll have to take logs of both sides. And since 10^x and logx will cancel out, you should get an answer for x.
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    There are methods to solve this numerically without a calculator, and by solve I mean approximate the solution to a chosen degree of accuracy,
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    (Original post by B_9710)
    There are methods to solve this numerically without a calculator, and by solve I mean approximate the solution to a chosen degree of accuracy,
    That is what I have been saying. Did you have ever do that without a calculator? I did! I need about 30 up tp 50 approximations to get a very precise value for some terms like this one.
 
 
 
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