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How do you solve #10^ { 7x } = 76#?

Answer 1

Sophie Adams

Solution: #x ~~ 0.269 #

#10^(7x) =76 # taking log on both sides we get ,

#7x log 10 =log 76 or 7x = log 76 (log10=1)# or

#7x= 1.8808 or x = 1.8808/7 ~~ 0.269 (3dp)#

Solution: #x ~~ 0.269 (3dp)# [Ans]

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Answer 2

Elias Ackerman

To solve (10^{7x} = 76), you would take the logarithm of both sides of the equation to isolate (x). Specifically, you would use the logarithm base 10, since the exponent in the equation is 10.

So, taking the logarithm base 10 of both sides:

[\log_{10}(10^{7x}) = \log_{10}(76)]

By the properties of logarithms, the logarithm of a number raised to an exponent is equal to the exponent times the logarithm of the base. Therefore:

[7x \cdot \log_{10}(10) = \log_{10}(76)]

Since (\log_{10}(10) = 1), the equation simplifies to:

[7x = \log_{10}(76)]

Finally, to solve for (x), divide both sides of the equation by 7:

[x = \frac{\log_{10}(76)}{7}]

You can then evaluate this expression to find the numerical value of (x).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.