Power raised to a logarithm question

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Homework Help Overview

The discussion revolves around solving the equation 7^log(base: 7) 3 = x, focusing on the properties of logarithms and exponents. Participants are exploring the relationship between powers and logarithmic functions.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Some participants attempt to relate the properties of logarithms and exponents, questioning how to manipulate the equation to isolate x. Others explore the concept of inverse functions in relation to logarithms.

Discussion Status

The discussion is ongoing, with participants sharing their thoughts on the properties of logarithms and exponents. There is a mix of attempts to clarify concepts and questions about the inverse relationships between functions.

Contextual Notes

Participants are engaging with the problem without providing a definitive solution, and there are indications of varying levels of understanding among them.

Coco12
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Homework Statement


Solve for x
7^log(base: 7) 3 = x

Homework Equations





The Attempt at a Solution


Ans is 3
Can someone explain to me how to solve for powers raised to a log like this one?
 
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y = 10 ^ x then log y = x right ?

looking at log y = x then 10 ^ log y = 10 ^ x

but 10 ^ x is y so

10 ^ log y = y

now since 10 is the base follow the same logic with base 7
 
in which grade are you??
 
Coco12 said:
Can someone explain to me how to solve for powers raised to a log like this one?
7x is a function: for every real number x, 7x has a single, well-defined value. Denote this function as f(x): f(x)=7x. Rhetorical question: What's the inverse of this function? The answer is log base 7. Denote this as f-1(x)=log7x.

A non-rhetorical question: Given *any* function f(x) and its inverse f-1(x), what is f(f-1(x)) ?
 

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