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To solve the equation $5^{x}=7,$ we must find the exponent to which 5 must be raised in order to obtain $7 .$ This is $\log _{5} 7$(a) Use the change-of-base rule and your calculator to find $\log _{5} 7$(b) Raise 5 to the number you found in part (a). What is your result?(c) Using as many decimal places as your calculator gives, write the solution set of $5^{x}=7$.
Algebra
Chapter 12
Inverse, Exponential, and Logarithmic Functions
Section 5
Common and Natural Logarithms
Functions
Exponential and Logarithmic Functions
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Okay, so report A We want to use our change, your baseball and our calculator to find log base 57 Well, we can use our change of base. This would be the natural log of stepping over the natural log of five. So it's bigger in your child. Okay, so that gives us 1.209 year old 61 No. Infighting five. Okay. And now we want to report be raise far into the number of part A. That's going to be five to depart of 12.209 Joe 61955 And now, let's plug this in. Do we have five to the power of, um, 1.209 061955 So this is equal to if we round that. That would be a seven Andi report. See, you want to right? The solutions that of Bob depart is equal to seven. Okay, so by matching part B two c, we see that our expert our needs to be our exponents of X is equal to 1.209 Joe 61955
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