Solve for x 5(10^(x-6))=7

Problem

5*(10(x−6))=7

Solution

1. Isolate the exponential term by dividing both sides of the equation by 5

10(x−6)=7/5

2. Convert the fraction to a decimal to simplify the expression.

10(x−6)=1.4

3. Apply the common logarithm ((log_10)() to both sides of the equation to move the variable out of the exponent.

(log_)(10(x−6))=(log_)(1.4)

4. Simplify the left side using the property (log_)(10)=u

x−6=(log_)(1.4)

5. Solve for x by adding 6 to both sides.

x=6+(log_)(1.4)

Final Answer

x=6+(log_)(1.4)

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